The number of arbitrary constants in the particular solution of a differential equation of second order is (are):
- ✓0
- B1
- C2
- D3
Answer: A.
View full solution →Question types
DIFFERENTIAL EQUATIONS question types
782 questions across 9 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
782
Questions
9
Question groups
5
Question types
01
M.C.Q (1 Marks)
176 Q→02Assertion (A) & Reason (B) MCQ
6 Q→031 Marks Question
63 Q→042 Marks Questions
35 Q→053 Marks Question
86 Q→065 Marks Questions
384 Q→07Case study (4 Marks)
10 Q→08Fill In The Blanks[1 Marks ]
11 Q→09True False[1 Marks ]
11 Q→Sample Questions
DIFFERENTIAL EQUATIONS questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The solution of the differential equation $dy = (1 + y^2) dx$ is:
- A$\text{y}=\tan\text{x}+\text{c}$
- ✓$\text{y}=\tan(\text{x}+\text{c})$
- C$\tan^{-1}(\text{y}+\text{c})=\text{x}$
- D$(\tan^{-1}(\text{y}+\text{c})=2\text{x})$
Answer: B.
View full solution →The degree and the order of the differential equation
$\text{y}=\text{x}\Big(\frac{\text{dy}}{\text{dx}}\Big)^2+\Big(\frac{\text{dx}}{\text{dy}}\Big)^2$ are respectively:
$\text{y}=\text{x}\Big(\frac{\text{dy}}{\text{dx}}\Big)^2+\Big(\frac{\text{dx}}{\text{dy}}\Big)^2$ are respectively:
- A1, 1
- B2, 1
- ✓4, 1
- D1, 4
Answer: C.
View full solution →The solution of the differential equation $\text{x}\frac{\text{dy}}{\text{dx}}=\text{y}+\text{x}\ \tan\frac{\text{y}}{\text{x}}$ is:
- ✓$\sin\frac{\text{x}}{\text{y}}=\text{x}+\text{C}$
- B$\sin\frac{\text{y}}{\text{x}}=\text{Cx}$
- C$\sin\frac{\text{x}}{\text{y}}=\text{Cy}$
- D$\sin\frac{\text{y}}{\text{x}}=\text{Cy}$
Answer: A.
View full solution →The degree of the differntial equation $\Big(\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}\Big)^{2}=\Big(\frac{\text{dy}}{\text{dx}}\Big)=\text{y}^{3}$ is:
- A$\frac{1}{2}$
- ✓$2$
- C$3$
- D$4$
Answer: B.
View full solution →Directions: In these questions, a statement of Assertion is followed by a statement of Reason is given.Choose the correct answer out of the following choices:
Assertion: If $\frac{\text{dy}}{\text{dy}}+\text{xy}=\text{x}^3\text{y}^3,\text{x}>0,\text{y}\geq0$ and $\text{y}(0)=1,$ then $\text{y}(1)=\frac{1}{\sqrt{2}}$
Reason: The differential equation is linear with integrating factor $e^x$
Assertion: If $\frac{\text{dy}}{\text{dy}}+\text{xy}=\text{x}^3\text{y}^3,\text{x}>0,\text{y}\geq0$ and $\text{y}(0)=1,$ then $\text{y}(1)=\frac{1}{\sqrt{2}}$
Reason: The differential equation is linear with integrating factor $e^x$
- AAssertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- BAssertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- ✓Assertion is correct statement but Reason is wrong statement.
- DAssertion is wrong statement but Reason is correct statement.
Answer: C.
View full solution →Directions : In these questions, a statement of Assertion is followed by a statement of Reason is given.Choose the correct answer out of the following choices :
Assertion : The elimination of four arbitrary constants in $\text{y}=(\text{c}_1+\text{c}_2+\text{c}_3\text{e}^\text{c}4)\text{x}$ results into a differential equation of the first order $\text{x}\frac{\text{dy}}{\text{dx}}=\text{y}$
Reason : Elimination of $n$ arbitrary constants requires in general, a differential equation of the $n^{th}$ order.
Assertion : The elimination of four arbitrary constants in $\text{y}=(\text{c}_1+\text{c}_2+\text{c}_3\text{e}^\text{c}4)\text{x}$ results into a differential equation of the first order $\text{x}\frac{\text{dy}}{\text{dx}}=\text{y}$
Reason : Elimination of $n$ arbitrary constants requires in general, a differential equation of the $n^{th}$ order.
- ✓Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- BAssertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- CAssertion is correct statement but Reason is wrong statement.
- DAssertion is wrong statement but Reason is correct statement.
Answer: A.
View full solution →Directions : In these questions, a statement of Assertion is followed by a statement of Reason is given.Choose the correct answer out of the following choices:
Assertion : Order of the differential equation whose solution is $\text{y}=\text{c}_1\text{e}^{\text{x}+\text{c}_2}+\text{c}_3\text{e}^{\text{x}+\text{c}_4}$ is $4.$
Reason : Order of the differential equation is equal to the number of independent arbitrary constants mentioned in the solution of the differential equation.
Assertion : Order of the differential equation whose solution is $\text{y}=\text{c}_1\text{e}^{\text{x}+\text{c}_2}+\text{c}_3\text{e}^{\text{x}+\text{c}_4}$ is $4.$
Reason : Order of the differential equation is equal to the number of independent arbitrary constants mentioned in the solution of the differential equation.
- AAssertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- BAssertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- CAssertion is correct statement but Reason is wrong statement.
- ✓Assertion is wrong statement but Reason is correct statement.
Answer: D.
View full solution →Directions : In these questions, a statement of Assertion is followed by a statement of Reason is given.Choose the correct answer out of the following choices:
Assertion : $\text{x}\sin\text{x}\frac{\text{dy}}{\text{dx}}+(\text{x}+\text{x}\cos\text{x}+\sin \text{x}) \text{y}=\sin\text{xy},$
$(\frac{\pi}{2}) =1-\frac{2}{\pi}\Rightarrow \lim\limits_{\text{x}\rightarrow0}\text{y(x)}=\frac{1}{3}.$
Reason : The differential equation is linear with integrating factor $\text{x}(1-\cos\text{x})$
Assertion : $\text{x}\sin\text{x}\frac{\text{dy}}{\text{dx}}+(\text{x}+\text{x}\cos\text{x}+\sin \text{x}) \text{y}=\sin\text{xy},$
$(\frac{\pi}{2}) =1-\frac{2}{\pi}\Rightarrow \lim\limits_{\text{x}\rightarrow0}\text{y(x)}=\frac{1}{3}.$
Reason : The differential equation is linear with integrating factor $\text{x}(1-\cos\text{x})$
- ✓Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- BAssertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- CAssertion is correct statement but Reason is wrong statement.
- DAssertion is wrong statement but Reason is correct statement.
Answer: A.
View full solution →Directions : In these questions, a statement of Assertion is followed by a statement of Reason is given.Choose the correct answer out of the following choices :
Assertion : The differential equation of all circles in a plane must be of order $3$.
Reason : If three points are non $-$ collinear, then only one circle passes through these points.
Assertion : The differential equation of all circles in a plane must be of order $3$.
Reason : If three points are non $-$ collinear, then only one circle passes through these points.
- AAssertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- ✓Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- CAssertion is correct statement but Reason is wrong statement.
- DAssertion is wrong statement but Reason is correct statement.
Answer: B.
View full solution →Find the sum of the order and the degree of the following differential equation:
$\text{y = x} \bigg(\frac{\text{dy}}{\text{dx}}\bigg)^{3} + \frac{\text{d}^{2}{\text{y}}}{\text{d}}$
View full solution →$\text{y = x} \bigg(\frac{\text{dy}}{\text{dx}}\bigg)^{3} + \frac{\text{d}^{2}{\text{y}}}{\text{d}}$
Find the solution of the following differential equation:
$\text{x}\sqrt{(1 + \text{y}^{2})} \text{dx + y} \sqrt{( 1 + \text{x}^{2})} \text{dy} = 0$
View full solution →$\text{x}\sqrt{(1 + \text{y}^{2})} \text{dx + y} \sqrt{( 1 + \text{x}^{2})} \text{dy} = 0$
Find the sum of the order and the degree of the following differential equation:
$\text{y = x} \bigg(\frac{\text{dy}}{\text{dx}}\bigg)^{3} + \frac{\text{d}^{2}{\text{y}}}{\text{dx}^2}$
View full solution →$\text{y = x} \bigg(\frac{\text{dy}}{\text{dx}}\bigg)^{3} + \frac{\text{d}^{2}{\text{y}}}{\text{dx}^2}$
Write the differential equation representing the family of curves y = mx, where m is an arbitrary constant.
Find the differential equation representing the family of curves $\text{v} = \frac{\text{A}}{\text{r}} + \text{B},$ where A and B are arbitrary constants.
View full solution →$\text{Find} \frac{\text{dy}}{\text{dx}} \text{at } x = 1, \text{y} = \frac{\pi}{4} \text{if } { \sin}^{2}\text{y} + \cos x\text{y = K}.$
View full solution →Find the differential equation representing the family of curves $y = ae^{bx+5}$, where a and b are arbitrary constants.
View full solution →Form the differential equation representing the family of curves $y = e^{2x}(a + bx)$, where ‘a’ and ‘b’ are arbitrary constants.
View full solution →Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\text{x}+\Big(\frac{\text{dy}}{\text{dx}}\Big)=\sqrt{1+\Big(\frac{\text{dy}}{\text{dx}}\Big)^2}$
View full solution →$\text{x}+\Big(\frac{\text{dy}}{\text{dx}}\Big)=\sqrt{1+\Big(\frac{\text{dy}}{\text{dx}}\Big)^2}$
Form the differential equation from the following primitives where constants are arbitrart:$\text{y}^2=4\text{ax}$
View full solution →Form the differential equation of the family of curves y = a cos(x + b), where a and b are arbitrary constants.
Solve the following differential equation:
$4\frac{\text{dy}}{\text{dx}}+\text{8y}=\text{5e}^{-3x}$.
View full solution →$4\frac{\text{dy}}{\text{dx}}+\text{8y}=\text{5e}^{-3x}$.
Solve the following differential equation:
$y(1 - x^2) \frac{\text{dy}}{\text{dx}} = x(1 + y^2)$.
View full solution →$y(1 - x^2) \frac{\text{dy}}{\text{dx}} = x(1 + y^2)$.
Verify that y = A cos x - b sin x is a solution of the differential equation.
$\frac{\text{d}^{2} \text{y}}{\text{dx}^{2}}+\text{y}=0.$
View full solution →$\frac{\text{d}^{2} \text{y}}{\text{dx}^{2}}+\text{y}=0.$
Solve the following differential equation:
$(y^2 - x^2) dy = 3xy\ dx$.
View full solution →$(y^2 - x^2) dy = 3xy\ dx$.
$\text{If}\cos^{-1}\frac{x}{\text{a}} + \cos^{-1}\frac{y}{\text{b}} = \alpha, \text{Prove that}\frac{{x}^{2}}{\text{a}^{2}} - 2\frac{xy}{\text{ab}}\cos\alpha +\frac{{y}^{2}}{\text{b}^{2}} = \sin^{2}\alpha$
View full solution →Find the general solution of the differential equation
$\frac{\text{dy}}{\text{dx}}-\text{y}=\sin\text{x}.$
View full solution →$\frac{\text{dy}}{\text{dx}}-\text{y}=\sin\text{x}.$
Find the particular solution of the differential equation $\text{(x - y)} \frac{\text{dy}}{\text{dx}} = \text{(x + 2y),}$ given that y = 0 when x = 1.
View full solution →Find the equations of the tangent and normal to the curve$\frac{\text{x}^{2}}{\text{a}^{2}} - \frac{\text{y}^{2}}{\text{b}^{2}} = 1$ at the point ($\sqrt{2}$a, b).
View full solution →If $y = P e^{ax}+ Q e^{bx},$ show that
$\frac{\text{d}^2\text{y}}{\text{dx}^2}-(\text{a}+\text{b})\frac{\text{dy}}{\text{dx}}+\text{aby}=0$
View full solution →$\frac{\text{d}^2\text{y}}{\text{dx}^2}-(\text{a}+\text{b})\frac{\text{dy}}{\text{dx}}+\text{aby}=0$
A differential equation is said to be in the variable separable form if it is expressible in the form $f(x) dx = g(y)$ dy.
The solution of this equation is given by
$\int\text{f(x)dx}=\int\text{g(y)dy}+\text{c},$ where c is the constant of integration.
Based on the above information, answer the following questions.
View full solution →The solution of this equation is given by
$\int\text{f(x)dx}=\int\text{g(y)dy}+\text{c},$ where c is the constant of integration.
Based on the above information, answer the following questions.
- If the solution of the differential equation $\frac{\text{dy}}{\text{dx}}=\frac{\text{ax+3}}{\text{2y+f}}$ represents a circle, then the value of $'a'$ is:
- $2$
- $-2$
- $3$
- $-4$
- The differential equation $\frac{\text{dy}}{\text{dx}}=\frac{\sqrt{1-\text{y}^2}}{\text{y}}$ determines a family of circle with.
- Variable radii and fixed centre $(0, 1)$
- Variable radii and fixed centre $(0, -1)$
- Fixed radius 1 and variable centre on $x-$axis
- Fixed radius 1 and variable centre on $y-$axis
- If $= y'+ 1, y(0) = 1,$ then $y ($In $2) =$
- $1$
- $2$
- $3$
- $4$
- The solution of the differential equation $\frac{\text{dy}}{\text{dx}}=\text{e}^\text{x-y}+\text{x}^2\text{e}^\text{-y}$ is:
- $\text{e}^\text{x}=\frac{\text{y}^3}{3}+\text{e}^\text{y}+\text{c}$
- $\text{e}^\text{y}=\frac{\text{x}^2}{3}+\text{e}^\text{x}+\text{c}$
- $\text{e}^\text{y}=\frac{\text{x}^3}{3}+\text{e}^\text{x}+\text{c}$
- None of these
- If $\frac{\text{dy}}{\text{dx}}=\text{y}\sin2\text{x},\ \text{y}(0)=1,$ then its solution is:
- $\text{y}=\text{e}^{\sin^2}\text{x}$
- $\text{y}={\sin^2}\text{x}$
- $\text{y}={\cos^2}\text{x}$
- $\text{y}=\text{e}^{\cos^2}\text{x}$
It is known that, if the interest is compounded continuously, the principal changes at the rate equal to the product of the rate of bank interest per annum and the principal. Let $P$ denotes the principal at any time t and rate of interest be $r\%$ per annum.
Based on the above information, answer the following question.
View full solution →Based on the above information, answer the following question.
- Find the value of $\frac{\text{dP}}{\text{dt}}.$
- $\frac{\text{Pr}}{1000}$
- $\frac{\text{Pr}}{100}$
- $\frac{\text{Pr}}{10}$
- $\text{Pr}$
- If $P_0$ be the initial principal, then find the solution of differential equation formed in given situation.
- $\log\Big(\frac{\text{P}}{\text{P}_0}\Big)=\frac{\text{rt}}{100}$
- $\log\Big(\frac{\text{P}}{\text{P}_0}\Big)=\frac{\text{rt}}{10}$
- $\log\Big(\frac{\text{P}}{\text{P}_0}\Big)=\text{rt}$
- $\log\Big(\frac{\text{P}}{\text{P}_0}\Big)=100\text{rt}$
- If the interest is compounded continuously at $5\%$ per annum, in how many years will $₹\ 100$ double itself?
- $12.728$ years
- $14.789$ years
- $13.862$ years
- $15.872$ years
- At what interest rate will $₹\ 100$ double itself in $10$ years? $(\log_\text{e}2 = 0.6931 ).$
- $9.66\%$
- $8.239\%$
- $7.341\%$
- $6.931\%$
- How much will $₹\ 1000$ be worth at $5\%$ interest after $10$ years? $(e^{0.5} = 1.648).$
- $₹\ 1648$
- $₹\ 1500$
- $₹\ 1664$
- $₹\ 1572$
Order: The order of a differential equation is the order of the highest order derivative appearing in the differential equation.
Degree: The degree of differential equation is the power of the highest order derivative, when differential coefficients are made free from radicals and fractions. Also, differential equation must be a polynomial equation in derivatives for the degree to be defined.
Based on the above information, answer the following questions.
View full solution →Degree: The degree of differential equation is the power of the highest order derivative, when differential coefficients are made free from radicals and fractions. Also, differential equation must be a polynomial equation in derivatives for the degree to be defined.
Based on the above information, answer the following questions.
- Find the degree of the differential equation $2\frac{\text{d}^2\text{y}}{\text{dx}^2}+3\sqrt{1-\Big(\frac{\text{dy}}{\text{dx}}\Big)^2-\text{y}=0}.$
- $3$
- $4$
- $3$
- $1$
- Order and degree of the differential equation $\text{y}\frac{\text{dy}}{\text{dx}}=\frac{\text{x}}{\frac{\text{dy}}{\text{dx}}+\Big(\frac{\text{dy}}{\text{dx}}\Big)^3}$ are respectively.
- $1, 1$
- $1, 2$
- $1, 3$
- $1, 4$
- Find order and degree of the equation $y'" + y^2 + e^{y'} = 0.$
- Order $= 3,$ degree $=$ undefined.
- Order $= 1,$ degree $= 3.$
- Order $= 2,$ degree $=$ undefined.
- Order $= 1,$ degree $= 2.$
- Determine degree of the differential equation $(\sqrt{\text{a+x}})\times\Big(\frac{\text{dy}}{\text{dx}}\Big)+\text{x}=0.$
- $3$
- Not defined
- $1$
- $2$
- Order and degree of the differential equation $\Bigg(1+\Big(\frac{\text{dy}}{\text{dx}}\Big)^3\Bigg)^\frac{7}{3}=7\frac{\text{d}^2\text{y}}{\text{dx}^2}$ are respectively.
- $2, 1$
- $2, 3$
- $1, 3$
- $1,\ \frac{7}{3}$
If an equation is of the form $\frac{\text{dy}}{\text{dx}}+\text{Py}=\text{Q},$ where P, Qare functions of x, then such equation is known as linear differential equation. Its solution is given by
$\text{y}\times\text{(I.F.)}=\int\text{Q}\times\text{(I.F.)}\text{dx}+\text{c},$ where $\text{I.F.}=\text{e}^{\int\text{pdx}}.$
Now, suppose the given equation is $(1+\sin\text{x})\frac{\text{dy}}{\text{dx}}+\text{y}\cos\text{x}+\text{x}=0.$
Based on the above information, answer the following questions.
View full solution →$\text{y}\times\text{(I.F.)}=\int\text{Q}\times\text{(I.F.)}\text{dx}+\text{c},$ where $\text{I.F.}=\text{e}^{\int\text{pdx}}.$
Now, suppose the given equation is $(1+\sin\text{x})\frac{\text{dy}}{\text{dx}}+\text{y}\cos\text{x}+\text{x}=0.$
Based on the above information, answer the following questions.
- The value of P and Q respectively are:
- $\frac{\sin\text{x}}{1+\cos\text{x}},\ \frac{\text{x}}{1+\sin\text{x}}$
- $\frac{\cos\text{x}}{1+\sin\text{x}},\ \frac{\text{-x}}{1+\sin\text{x}}$
- $\frac{-\cos\text{x}}{1+\sin\text{x}},\ \frac{\text{x}}{1+\sin\text{x}}$
- $\frac{\cos\text{x}}{1+\sin\text{x}},\ \frac{\text{x}}{1+\sin\text{x}}$
- The value of I.F is:
- $1-\sin\text{x}$
- $\cos\text{x}$
- $1+\sin\text{x}$
- $1-\cos\text{x}$
- Solution of given equation is:
- $\text{y}(1-\sin\text{x})=\text{x+c}$
- $\text{y}(1+\sin\text{x})=-\text{x}^2+\text{c}$
- $\text{y}(1-\sin\text{x})=\frac{\text{-x}^2}{2}\text{+c}$
- $\text{y}(1+\sin\text{x})=\frac{\text{-x}^2}{2}\text{+c}$
- If y(0) = 1, then y equals
- $\frac{2-\text{x}^2}{2(1+\sin\text{x})}$
- $\frac{2+\text{x}^2}{2(1+\sin\text{x})}$
- $\frac{2-\text{x}^2}{2(1-\sin\text{x})}$
- $\frac{2+\text{x}^2}{2(1-\sin\text{x})}$
- Value of is $\text{y}\Big(\frac{\pi}{2}\Big)$ is:
- $\frac{4-\pi^2}{2}$
- $\frac{8-\pi^2}{16}$
- $\frac{8-\pi^2}{4}$
- $\frac{4+\pi^2}{2}$
If the equation is of the form $\frac{\text{dy}}{\text{dx}}=\frac{\text{f(x, y)}}{\text{g(x, y)}}$or $\frac{\text{dy}}{\text{dx}}=\text{F}\Big(\frac{\text{y}}{\text{x}}\Big),$ where f(x, y), g(x, y) are homogeneous functions of the same degree in x and y, then put y = vx and $\frac{\text{dy}}{\text{dx}}=\text{v+x}\Big(\frac{\text{dv}}{\text{dx}}\Big),$ so that the dependent variable y is changed to another variable v and then apply variable separable method.
Based on the above information, answer the following questions.
View full solution →Based on the above information, answer the following questions.
- The general solution of $\text{x}^2\frac{\text{dy}}{\text{dx}}=\text{x}^2+\text{xy}+\text{y}^2$ is:
- $\tan^{-1}\frac{\text{x}}{\text{y}}=\log|\text{x}|+\text{c}$
- $\tan^{-1}\frac{\text{y}}{\text{x}}=\log|\text{x}|+\text{c}$
- $\text{y}=\text{x}\log|\text{x}|+\text{c}$
- $\text{x}=\text{y}\log|\text{y}|+\text{c}$
- Solution of the differential equation $2\text{xy}\frac{\text{dy}}{\text{dx}}=\text{x}^2+3\text{y}^2$ is:
- $x^3 + y^2 = cx^2$
- $\frac{\text{x}^2}{2}+\frac{\text{y}^3}{3}=\text{y}^2+\text{c}$
- $x^2 + y^3 = cx^2$
- $x^2 + y^2 = cx^3$
- General solution of the differential equation $(x^2 + 3xy + y^2) dx - x^2 dy = 0$ is:
- $\frac{\text{x+y}}{\text{y}}-\log\text{x = c}$
- $\frac{\text{x+y}}{\text{y}}+\log\text{x = c}$
- $\frac{\text{x}}{\text{x+y}}-\log\text{x = c}$
- $\frac{\text{x}}{\text{x+y}}+\log\text{x = c}$
- General solution of the differential equation $\frac{\text{dy}}{\text{dx}}=\frac{\text{y}}{\text{x}}\bigg\{\log\Big(\frac{\text{y}}{\text{x}}\Big)+1\bigg\}$ is:
- $\log(\text{xy})=\text{c}$
- $\log\text{y}=\text{cx}$
- $\log\frac{\text{y}}{\text{x}}=\text{cx}$
- $\log\text{x}=\text{cy}$
- Solution of the differential equation $\Big(\text{x}\frac{\text{dy}}{\text{dx}}-\text{y}\Big)\text{e}^\frac{\text{y}}{\text{x}}=\text{x}^2\ \cos\text{x}$ is:
- $\text{e}^\frac{\text{y}}{\text{x}}-\sin\text{x = c}$
- $\text{e}^\frac{\text{y}}{\text{x}}+\sin\text{x = c}$
- $\text{e}^\frac{\text{-y}}{\text{x}}-\sin\text{x = c}$
- $\text{e}^\frac{\text{-y}}{\text{x}}+\sin\text{x = c}$
Fill in the blanks.
The solution of the differential equation $\text{x}\frac{\text{dy}}{\text{dx}}+2\text{y}=\text{x}^2$ is ________.
View full solution →The solution of the differential equation $\text{x}\frac{\text{dy}}{\text{dx}}+2\text{y}=\text{x}^2$ is ________.
Fill in the blanks.
The solution of the differential equation $\text{ydx}+(\text{x}+\text{xy})\text{dy}=0$ is ________.
View full solution →The solution of the differential equation $\text{ydx}+(\text{x}+\text{xy})\text{dy}=0$ is ________.
Fill in the blanks.
The integrating factor of $\frac{\text{dy}}{\text{dx}}+\text{y}=\frac{1+\text{y}}{\text{x}}$ is ________.
View full solution →The integrating factor of $\frac{\text{dy}}{\text{dx}}+\text{y}=\frac{1+\text{y}}{\text{x}}$ is ________.
Fill in the blanks.
The number of arbitrary constants in the general solution of a differential equation of order three is ________.
The number of arbitrary constants in the general solution of a differential equation of order three is ________.
Fill in the blanks.
The solution of differential equation $\cot\text{y dx}=\text{x dy} $ is _________.
View full solution →The solution of differential equation $\cot\text{y dx}=\text{x dy} $ is _________.
State True or False for the following:
The differential equation representing the family of circles $x^2+(y-a)^2=a^2$ will be of order two.
View full solution →The differential equation representing the family of circles $x^2+(y-a)^2=a^2$ will be of order two.
State True or False for the following:
The solution of the differential equation $\frac{\text{dy}}{\text{dx}}=\frac{\text{x}+2\text{y}}{\text{x}}$ is $\text{x}+\text{y}=\text{k}\text{x}^2.$
View full solution →The solution of the differential equation $\frac{\text{dy}}{\text{dx}}=\frac{\text{x}+2\text{y}}{\text{x}}$ is $\text{x}+\text{y}=\text{k}\text{x}^2.$
State True or False for the following:
Solution of $\frac{\text{xdy}}{\text{dx}}=\text{y}+\text{x}\tan\Big(\frac{\text{y}}{\text{x}}\Big)$ is $\sin\Big(\frac{\text{y}}{\text{x}}\Big)=\text{cx}.$
View full solution →Solution of $\frac{\text{xdy}}{\text{dx}}=\text{y}+\text{x}\tan\Big(\frac{\text{y}}{\text{x}}\Big)$ is $\sin\Big(\frac{\text{y}}{\text{x}}\Big)=\text{cx}.$
State True or False for the following:
The differential equation of all non horizontal lines in a plane is $\frac{\text{d}^2\text{x}}{\text{d}\text{y}^2}=0.$
View full solution →The differential equation of all non horizontal lines in a plane is $\frac{\text{d}^2\text{x}}{\text{d}\text{y}^2}=0.$
State True or False for the following:
Number of arbitrary constants in the particular solution of a differential equation of order two is two.
Number of arbitrary constants in the particular solution of a differential equation of order two is two.
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