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Differential Equations MATHS - Differential Equations

Rajasthan Board (RBSE) - STD 12 Science - MATHS (Rajasthan - English Medium). 436 questions in this chapter.

Question types

Differential Equations question types

436 questions across 5 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

436
Questions
5
Question groups
5
Question types
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.

Q 1M.C.Q (1 Marks)1 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:
  1. $\sin\frac{\text{x}}{\text{y}}=\text{x}+\text{C}$
  2. $\sin\frac{\text{y}}{\text{x}}=\text{Cx}$
  3. $\sin\frac{\text{x}}{\text{y}}=\text{Cy}$
  4. $\sin\frac{\text{y}}{\text{x}}=\text{Cy}$ 
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Q 2M.C.Q (1 Marks)1 Mark
The solution of the differential equation $2\text{x}\frac{\text{dy}}{\text{dx}}-\text{y}=3$ resresents:
  1. circles
  2. straight lines
  3. ellipses
  4. parabolas
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Q 3M.C.Q (1 Marks)1 Mark
The solution of the differential equation $\frac{\text{dy}}{\text{dx}}-\text{Ky}=0, \text{y}(0)=1$ approaches to zero when $\text{x}\rightarrow\propto$ if,
  1. K = 0
  2. K > 0
  3. K < 0
  4. None of these.
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Q 4M.C.Q (1 Marks)1 Mark
The differential equation satisfied by $\text{ax}^{2}+\text{by}^{2}=1$ is:
  1. $\text{xyy}_{2}+\text{y}_{1}^{2}+\text{yy}_{1}=0$
  2. $\text{xyy}_{2}+\text{xy}_{1}^{2}-\text{yy}_{1}=0$
  3. $\text{xyy}_{2}+\text{xy}_{1}^{2}+\text{yy}_{1}=0$
  4. None of these. 
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Q 5M.C.Q (1 Marks)1 Mark
The order of the differential whose general solution is given by ${\text{y}}=\text{C}_1\cos(2\text{x}+\text{C}_{2}) (\text{C}_{3}+\text{C}_{4})\text{a}^{\text{x}+\text{C}_{5}}+\text{C}_{6}\sin(\text{x}-\text{C}_{7}).$
  • A
    $3$
  • B
    $4$
  • ✓
    $5$
  • D
    $2$

Answer: C.

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Q 61 Marks Question1 Mark
Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$(\text{y"})^2+(\text{y})^3+\sin\text{y}=0$
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Q 71 Marks Question1 Mark
Write the degree of the differrntial equation $\text{x}^{3}\Big(\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}\Big)^{2}+\text{x}\Big(\frac{\text{dy}}{\text{dx}}\Big)^{4}=0.$ 
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Q 81 Marks Question1 Mark
Write the degree of the differrntial equation $\Big(\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}\Big)^{2}+\Big(\frac{\text{dy}}{\text{dx}}\Big)^{2}=\text{x}\sin\Big(\frac{\text{dy}}{\text{dx}}\Big).$ 
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Q 91 Marks Question1 Mark
Write the degree of the differrntial equation $\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}+\Big(\frac{\text{dy}}{\text{dx}}\Big)^{\frac{1}{4}}+\text{x}^{\frac{1}{5}}=0.$ 
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Q 112 Marks Questions2 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 225 Marks Questions5 Marks
Find the equation of the curve which passes through the point (1, 2) and the distance between the foot of the ordinate of the point of contact and the point of intersection of the tangent with x-axis twice abscissa of the pont of contact.
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