## NCERT Solutions for Class 12 Maths Chapter 9 – Differential Equations Ex 9.3

#### Question 1:

Differentiating both sides of the given equation with respect to x, we get:
Again, differentiating both sides with respect to x, we get:
Hence, the required differential equation of the given curve is

#### Question 2:

Differentiating both sides with respect to x, we get:
Again, differentiating both sides with respect to x, we get:
Dividing equation (2) by equation (1), we get:
This is the required differential equation of the given curve.

#### Question 3:

Differentiating both sides with respect to x, we get:
Again, differentiating both sides with respect to x, we get:
Multiplying equation (1) with (2) and then adding it to equation (2), we get:
Now, multiplying equation (1) with 3 and subtracting equation (2) from it, we get:
Substituting the values of in equation (3), we get:
This is the required differential equation of the given curve.

#### Question 4:

Differentiating both sides with respect to x, we get:
Multiplying equation (1) with 2 and then subtracting it from equation (2), we get:
y’-2y=e2x2a+2bx+b-e2x2a+2bx⇒y’-2y=be2x                                      …(3)
Differentiating both sides with respect to x, we get:
y”-2y’=2be2x                        …4Dividing equation (4) by equation (3), we get:
This is the required differential equation of the given curve.

#### Question 5:

Differentiating both sides with respect to x, we get:
Again, differentiating with respect to x, we get:
Adding equations (1) and (3), we get:
This is the required differential equation of the given curve.

#### Question 6:

Form the differential equation of the family of circles touching the y-axis at the origin.

The centre of the circle touching the y-axis at origin lies on the x-axis.
Let (a, 0) be the centre of the circle.
Since it touches the y-axis at origin, its radius is a.
Now, the equation of the circle with centre (a, 0) and radius (a) is
Differentiating equation (1) with respect to x, we get:
Now, on substituting the value of a in equation (1), we get:
This is the required differential equation.

#### Question 7:

Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.

The equation of the parabola having the vertex at origin and the axis along the positive y-axis is:
Differentiating equation (1) with respect to x, we get:
Dividing equation (2) by equation (1), we get:
This is the required differential equation.

#### Question 8:

Form the differential equation of the family of ellipses having foci on y-axis and centre at origin.

The equation of the family of ellipses having foci on the y-axis and the centre at origin is as follows:
Differentiating equation (1) with respect to x, we get:
Again, differentiating with respect to x, we get:
Substituting this value in equation (2), we get:
This is the required differential equation.

#### Question 9:

Form the differential equation of the family of hyperbolas having foci on x-axis and centre at origin.

The equation of the family of hyperbolas with the centre at origin and foci along the x-axis is:
Differentiating both sides of equation (1) with respect to x, we get:
Again, differentiating both sides with respect to x, we get:
Substituting the value ofin equation (2), we get:
This is the required differential equation.

#### Question 10:

Form the differential equation of the family of circles having centre on y-axis and radius 3 units.

Let the centre of the circle on y-axis be (0, b).
The differential equation of the family of circles with centre at (0, b) and radius 3 is as follows:
Differentiating equation (1) with respect to x, we get:
Substituting the value of (y – b) in equation (1), we get:
This is the required differential equation.

#### Question 11:

Which of the following differential equations hasas the general solution?
A.
B.
C.
D.

The given equation is:
Differentiating with respect to x, we get:
Again, differentiating with respect to x, we get:
This is the required differential equation of the given equation of curve.
Hence, the correct answer is B.

#### Question 12:

Which of the following differential equation hasas one of its particular solution?
A.
B.
C.
D.