# NCERT solution class 12 chapter 3 Differential Equations exercise 3.2 mathematics part 2

## EXERCISE 3.2

#### Question 1:  Differentiating both sides of this equation with respect to x, we get: Now, differentiating equation (1) with respect to x, we get: Substituting the values of in the given differential equation, we get the L.H.S. as: Thus, the given function is the solution of the corresponding differential equation.

#### Question 2:  Differentiating both sides of this equation with respect to x, we get: Substituting the value of in the given differential equation, we get:

L.H.S. = = R.H.S.

Hence, the given function is the solution of the corresponding differential equation.

#### Question 3:  Differentiating both sides of this equation with respect to x, we get: Substituting the value of in the given differential equation, we get:

L.H.S. = = R.H.S.

Hence, the given function is the solution of the corresponding differential equation.

#### Question 4:  Differentiating both sides of the equation with respect to x, we get:  L.H.S. = R.H.S.

Hence, the given function is the solution of the corresponding differential equation.

#### Question 5:  Differentiating both sides with respect to x, we get: Substituting the value of in the given differential equation, we get: Hence, the given function is the solution of the corresponding differential equation.

#### Question 6:  Differentiating both sides of this equation with respect to x, we get: Substituting the value of in the given differential equation, we get: Hence, the given function is the solution of the corresponding differential equation.

#### Question 7:  Differentiating both sides of this equation with respect to x, we get:  L.H.S. = R.H.S.

Hence, the given function is the solution of the corresponding differential equation.

#### Question 8:  Differentiating both sides of the equation with respect to x, we get: Substituting the value of in equation (1), we get: Hence, the given function is the solution of the corresponding differential equation.

#### Question 9:  Differentiating both sides of this equation with respect to x, we get: Substituting the value of in the given differential equation, we get: Hence, the given function is the solution of the corresponding differential equation.

#### Question 10:  Differentiating both sides of this equation with respect to x, we get: Substituting the value of in the given differential equation, we get: Hence, the given function is the solution of the corresponding differential equation.

#### Question 11:

The numbers of arbitrary constants in the general solution of a differential equation of fourth order are:

(A) 0 (B) 2 (C) 3 (D) 4

We know that the number of constants in the general solution of a differential equation of order n is equal to its order.

Therefore, the number of constants in the general equation of fourth order differential equation is four.

Hence, the correct answer is D.

#### Question 12:

The numbers of arbitrary constants in the particular solution of a differential equation of third order are:

(A) 3 (B) 2 (C) 1 (D) 0 