## EXERCISE 3.2

#### Page No 385:

#### Question 1:

#### Answer:

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 ofin 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:

#### Answer:

Differentiating both sides of this equation with respect to *x*, we get:

Substituting the value ofin 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:

#### Answer:

Differentiating both sides of this equation with respect to *x*, we get:

Substituting the value ofin 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:

#### Answer:

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:

#### Answer:

Differentiating both sides with respect to *x*, we get:

Substituting the value ofin the given differential equation, we get:

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

#### Question 6:

#### Answer:

Differentiating both sides of this equation with respect to *x*, we get:

Substituting the value ofin the given differential equation, we get:

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

#### Question 7:

#### Answer:

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:

#### Answer:

Differentiating both sides of the equation with respect to *x*, we get:

Substituting the value ofin equation (1), we get:

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

#### Question 9:

#### Answer:

Differentiating both sides of this equation with respect to *x*, we get:

Substituting the value ofin the given differential equation, we get:

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

#### Question 10:

#### Answer:

Differentiating both sides of this equation with respect to *x*, we get:

Substituting the value ofin 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

#### Answer:

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

#### Answer:

In a particular solution of a differential equation, there are no arbitrary constants.

Hence, the correct answer is D.