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.

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 quizzes

• Differentiation

Browse all Calculus quizzes