Differential Equation Case Study Questions Class 12

MCQ Questions

1. 1. The number of arbitrary constants in a family of curves equals the:

   1. Degree of the differential equation
   2. Order of the differential equation
   3. Number of variables
   4. Power of the highest derivative
2. 2. The differential equation formed by eliminating constants from \( y = A e^{2x} + B e^{-2x} \) is:

   1. \( \frac{dy}{dx} + 2y = 0 \)
   2. \( \frac{d^2y}{dx^2} – 4y = 0 \)
   3. \( \frac{d^2y}{dx^2} + 4y = 0 \)
   4. \( \frac{dy}{dx} – 4y = 0 \)
3. 3. Which method is used to form a differential equation from a family of curves?

   1. Elimination of variables
   2. Elimination of derivatives
   3. Elimination of arbitrary constants
   4. Substitution method
4. 4. The order of the differential equation formed from \( y = A \sin x + B \cos x \) is:

   1. 1
   2. 2
   3. 3
   4. 0
5. 5. Which of the following is the correct differential equation formed from \( y = A + Bx \)?

   1. \( \frac{dy}{dx} = B \)
   2. \( \frac{d^2y}{dx^2} = 0 \)
   3. \( \frac{dy}{dx} = A \)
   4. \( \frac{dy}{dx} = x \)