Differential Equations - Maharashtra Board STD 12 Maths Questions

Q 1MCQ1 Mark

The solution of the differential equation $\text{x}\frac{\text{dy}}{\text{dx}}=\text{y}+\text{x}\ \tan\frac{\text{y}}{\text{x}}$ is:

A
$\sin\frac{\text{x}}{\text{y}}=\text{x}+\text{C}$
✓
$\sin\frac{\text{y}}{\text{x}}=\text{Cx}$
C
$\sin\frac{\text{x}}{\text{y}}=\text{Cy}$
D
$\sin\frac{\text{y}}{\text{x}}=\text{Cy}$

Answer: B.

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Q 2MCQ1 Mark

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.

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Q 3MCQ1 Mark

Which of the following differentials equation has $y = x$ as one of its particular solution?

A
$\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}-\text{x}^{2}\frac{\text{dy}}{\text{dx}}+\text{xy}=\text{x}$
B
$\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}+\text{x}^{2}\frac{\text{dy}}{\text{dx}}+\text{xy}=\text{x}$
✓
$\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}-\text{x}^{2}\frac{\text{dy}}{\text{dx}}+\text{xy}=\text{0}$
D
$\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}+\text{x}^{2}\frac{\text{dy}}{\text{dx}}+\text{xy}=\text{0}$

Answer: C.

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Q 4MCQ1 Mark

The solution of the differential equartion $\frac{\text{dy}}{\text{dx}}-\frac{\text{y}(\text{x}+1)}{\text{x}}=0$ is given by:

✓
$\text{y}=\text{xe}^{\text{x}+\text{C}}$
B
$\text{x}=\text{ye}^{\text{x}}$
C
$\text{y}=\text{x}+\text{c}$
D
$\text{xy}=\text{e}^{\text{x}}+\text{C}$

Answer: A.

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Q 5MCQ1 Mark

A homogeneous dofferential equation of the from $\frac{\text{dx}}{\text{dy}}=\text{h}(\frac{\text{x}}{\text{y}})$ can be solved by making the substitution:

A
$y = vx$
B
$v = yx$
✓
$x = vy$
D
$x = v$

Answer: C.

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Q 6Answer the following questions in short.1 Mark

How many arbitray constants are there in the genral solution of the differential equation of orader 3.

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Q 7Answer the following questions in short.1 Mark

Write the order of the differential equation of all non-horizontal lines in a plane.

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Q 8Answer the following questions in short.1 Mark

Write the differential equation obtained emliminating the arbitrary constant $C$ in the equation $xy = C^2$.

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Q 9Answer the following questions in short.1 Mark

Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\sqrt{1-\text{y}^2}\text{dx}+\sqrt{1-\text{x}^2}\text{dx}=0$

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Q 10Answer the following questions in short.1 Mark

Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\frac{\text{d}^2\text{y}}{\text{dx}^2}+5\text{x}\Big(\frac{\text{dy}}{\text{dx}}\Big)-6\text{y}=\log\text{x}$

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Q 11Solve the Following Question.(2 Marks)2 Marks

Solve the following differential equation
$\frac{\text{dy}}{\text{dx}}=\text{e}^{\text{x}+\text{y}}+\text{x}^2\text{e}^\text{y}$

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Q 12Solve the Following Question.(2 Marks)2 Marks

Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\text{x}+\Big(\frac{\text{dy}}{\text{dx}}\Big)=\sqrt{1+\Big(\frac{\text{dy}}{\text{dx}}\Big)^2}$

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Q 13Solve the Following Question.(2 Marks)2 Marks

Form the differential equation from the following primitives where constants are arbitrart:$\text{y}^2=4\text{ax}$

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Q 14Solve the Following Question.(2 Marks)2 Marks

Represent the following families of curves by forming the corresponding differential equation:
$\text{x}^2-\text{y}^2=\text{a}^2$

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Q 15Solve the Following Question.(2 Marks)2 Marks

Solve the following differential equations:
$\frac{\text{dy}}{\text{dx}}=(\cos^2\text{x}-\sin^2\text{x})\cos^2\text{y}$

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Q 16Solve the Following Question.(3 Marks)3 Marks

Form the differential equation corresponding to $\text{y}^2=\text{a}(\text{b}-\text{x}^2)$ bt eliminating a and b.

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Q 17Solve the Following Question.(3 Marks)3 Marks

Solve the following differential equation
$\frac{\text{dy}}{\text{dx}}=\frac{1-\cos2\text{y}}{1+\cos2\text{y}}$

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Q 18Solve the Following Question.(3 Marks)3 Marks

Solve the following differential equations:
$\frac{\text{dy}}{\text{dx}}=2\text{xy, y}(0)=1$

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Q 19Solve the Following Question.(3 Marks)3 Marks

Find the equation of the curve which passes through the origin and has the slope x + 3y − 1 at any point (x, y) on it.

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Q 20Solve the Following Question.(3 Marks)3 Marks

Solve the following differential equations:$\frac{\text{dy}}{\text{dx}}+\frac{\cos\text{x}\sin\text{y}}{\cos\text{y}}=0$

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Q 21Solve the Following Question.(5 Marks)5 Marks

Represent the following families of curves by forming the corresponding differential equation:
$\frac{\text{x}^2}{\text{a}^2}-\frac{\text{y}^2}{\text{b}^2}=1$

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Q 22Solve the Following Question.(5 Marks)5 Marks

Solve the following differential equation:
$\frac{\text{dy}}{\text{dx}}+2\text{y}=\sin\text{x}$

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Q 23Solve the Following Question.(5 Marks)5 Marks

Form the differential equation of the family of circle in the secound qudrant and touching the coordinate axes.

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Q 24Solve the Following Question.(5 Marks)5 Marks

Solve the following initial value problems:
$(1+\text{y}^2)\text{dx}+(\text{x}-\text{e}^{\tan^{-1}\text{y}})\text{dy}=0,\text{ y}(0)=0$

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Q 25Solve the Following Question.(5 Marks)5 Marks

Form the differential equation of the family of curves represented by the equation (a being the perimeter):$(2\text{x}-\text{a})^2-\text{y}^2=\text{a}^2$

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Differential Equations question types

Differential Equations questions

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Differential Equations Maths - Differential Equations

Differential Equations question types

Differential Equations questions

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