Differential Equations Quiz - CBSE Class 12 Mathematics

Free practice quiz: Differential Equations (CBSE Class 12 Mathematics). 19 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 12 Mathematics practice quiz has 19 multiple-choice questions on Differential Equations, and 19 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. Find the order and degree of the differential equation: (d²y/dx²)³ + 2(dy/dx)⁴ + y = 0

   1. Order: 2, Degree: 3
   2. Order: 3, Degree: 2
   3. Order: 1, Degree: 4
   4. Order: 4, Degree: 1
   Show answer

   Answer: A. Order: 2, Degree: 3

   The order of a differential equation is the order of the highest derivative present. The degree is the power of the highest order derivative, after the equation has been made free from radicals and fractions.

2. Solve the differential equation: dy/dx + y = e⁻ˣ

   1. y = xe⁻ˣ + Ce⁻ˣ
   2. y = e⁻ˣ + Ceˣ
   3. y = xe⁻ˣ + Ceˣ
   4. y = eˣ + Ce⁻ˣ
   Show answer

   Answer: A. y = xe⁻ˣ + Ce⁻ˣ

   This is a first-order linear differential equation. Use an integrating factor to solve.

3. Solve the exact differential equation: (2x + y)dx + (x + 2y)dy = 0

   1. x² + xy + y² = C
   2. x + y = C
   3. x² + 2xy + y² = C
   4. x² + xy + 2y² = C
   Show answer

   Answer: A. x² + xy + y² = C

   Check for exactness (∂M/∂y = ∂N/∂x). If exact, integrate to find the solution.

4. Solve the differential equation: d²y/dx² + ω²y = 0

   1. y = Acos(ωx) + Bsin(ωx)
   2. y = Ae^(ωx) + Be^(-ωx)
   3. y = Acosh(ωx) + Bsinh(ωx)
   4. y = Ax + B
   Show answer

   Answer: A. y = Acos(ωx) + Bsin(ωx)

   This is a second-order linear homogeneous differential equation with constant coefficients. The characteristic equation has complex roots.

5. Solve the differential equation using Laplace transforms: y'' + 4y' + 4y = 0, y(0) = 1, y'(0) = 0

   1. y = (1+t)e⁻²ᵗ
   2. y = e⁻²ᵗ
   3. y = e²ᵗ
   4. y = (1-t)e⁻²ᵗ
   Show answer

   Answer: A. y = (1+t)e⁻²ᵗ

   Take the Laplace transform of the equation, solve for Y(s), and then find the inverse Laplace transform.

More questions in this quiz

Answers and explanations are in the full quiz.

1. Solve the differential equation: dy/dx = x² + 1
2. What is the general solution of a homogeneous linear differential equation?
3. Determine the integrating factor for the differential equation: x dy/dx + 2y = x²
4. Which of the following is a Bernoulli differential equation?
5. Find the particular solution of dy/dx = 2xy, given y(0) = 1.
6. What type of differential equation is (dy/dx)² + 2y = x?
7. Solve the differential equation: d²y/dx² - 4dy/dx + 4y = 0
8. A tank contains 100 liters of salt solution with 5 kg of salt. Pure water is poured into the tank at a rate of 5 L/min, and the mixture flows out at the same rate. Set up the differential equation for the amount of salt in the tank at time t.
9. What is the general solution to a non-homogeneous linear differential equation?
10. Use the method of undetermined coefficients to find a particular solution to y'' - y' - 6y = 2e^(3x)
11. Find the Laplace transform of f(t) = t²e⁻ᵗ.
12. A mass-spring system is modeled by the differential equation my'' + ky = 0. What is the solution if m = 1 and k = 4?
13. Solve the system of differential equations: dx/dt = 2x - y, dy/dt = x + 2y
14. What is the order of the differential equation that describes the motion of a damped harmonic oscillator?

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