## NCERT Solutions for Class 12 Maths Chapter 9 – Differential Equations Ex 9.2

#### 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 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:

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:

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:

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 ofin 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 ofin 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 ofin 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 ofin 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 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

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