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

## EXERCISE 3.2

#### 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.

#### 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.

#### 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.

#### 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.

#### 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.

#### 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.

#### 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.

#### 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.

#### 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.

#### 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.

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