Daily Practice Problems
Class 12 Maths
Differential Equations

Question 1:

Determine order and degree (if defined) of differential equation (y′′′)2 + (y″)3 + (y′)4 + y5 = 0

Question 2:

Solve the differential equation: (x2 - 1) * dy/dx + 2xy = 2/(x2 - 1)

Question 3:

Form the differential equation representing the family of curves

y = a sin(x + b), where a, b are arbitrary constants.

Question 4:

Find the general solution of the differential equation dy/dx + √{(1 – y2)/(1 – x2)} = 0

Question 5:

Find the differential equation of the family of lines through the origin.

Question 6:

Find a particular solution of the differential equation (x - y)(dx + dy) = dx – dy, given that y = -1, when x = 0.

Question: 7

Form the differential equation representing the family of curves

y = a sin(3x – b), where a and b are arbitrary constants.

Question 8:

Find the general solution of the differential equation

cos(dy/dx) = a (a R); y = 1 when x = 0.

Question 9:

Find the general solution of the differential equation:

x * dy/dx + y – x + xy cot x = 0 (x ≠ 0)

Question 10:

Prove that (x2 - y2) = c(x2 - y2)2 is the general solution of differential equation

(x3 – 3xy2)dx = (y3 – 3x2y)dy, where c is a parameter.

Question 11:

Verify that the function y = a cos x + b sin x, where, a, b R is a solution of the differential equation d2y/dx2 + y = 0.

Question 12:

For each of the given differential equation, find a particular solution satisfying the given condition: dy/dx = y * tan x; y = 1 when x = 0

Question 13:

Find the general solution of the differential equation dy/dx = (1 + y2)/(1 + x2).

Question 14:

Integrating factor of the differential equation (1 – x2)dy/dx – xy = 1 is ____.

Question 15:

Determine order and degree (if defined) of differential equation

y’’’ + 2y’’ + y’ = 0

Question 16:

Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:

y = √(1 + x2)                 :                 y’ = xy/(1 + x2)

Question 17:

Solve: cos(dy/dx) = a (a R); y = 1 when x = 0

Question 18:

Solve: dy/dx = 1 + x + y + xy

Question 19:

Write the general solution of differential equation:

dy/dx = ex+y

Question 20:

Form the differential equation representing the family of curves:

y = e2x(a + bx), where ‘a’ and ‘b’ are arbitrary constants.

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