Class 12 Differential Equations worksheet

Sample questions

Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.

Section A · multiple choice

1. 1.

   The order and degree of the differential equation (y′)³ + 9y + 9 = 0 are:

   1. order 1, degree 3
   2. order 3, degree 1
   3. order 1, degree 4
   4. order 2, degree 3

   Answer

   (a) order 1, degree 3

   highest derivative y′, raised to the power 3

2. 2.

   The general solution of dy/dx = 2x is:

   1. y = (2/3)x³ + C
   2. y = 2 + C
   3. y = x² + C
   4. y = 2x² + C

   Answer

   (c) y = x² + C

   integrate both sides

3. 3.

   The integrating factor of dy/dx − (1/x)y = x⁵ is:

   1. −log x
   2. x
   3. 1/x
   4. e⁻ˣ

   Answer

   (c) 1/x

   e^(∫P dx) with P = −1/x

Section B · short answer

1. 4.

   Solve dy/dx = 7x²/(9y³).

   Answer

   (9/4)y⁴ = (7/3)x³ + C

   9y³ dy = 7x² dx

2. 5.

   Solve dy/dx = 5y, given y = 8 when x = 0.

   Answer

   y = 8e⁵ˣ

   y = Ce⁵ˣ; x = 0 gives C = 8

Section C · long answer

1. 6.

   Solve dy/dx + 4y = −9e²ˣ, given y = 1 when x = 0.

   Answer

   y = −(3/2)e²ˣ + (5/2)e⁻⁴ˣ

   integrating factor e⁴ˣ: ye⁴ˣ = −(3/2)e⁶ˣ + C; C = 1 − (−3/2) = 5/2

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