NCERT Solutions for Maths Class 12 Exercise 9.5

Hello Students. In this post, you will find the complete NCERT Solutions for Maths Class 12 Exercise 9.5.

You can download the PDF of NCERT Books Maths Chapter 9 for your easy reference while studying NCERT Solutions for Maths Class 12 Exercise 9.5.

All the schools affiliated with CBSE, follow the NCERT books for all subjects. You can check your syllabus from NCERT Syllabus for Mathematics Class 12.

If you want to recall All Maths Formulas for Class 12, you can find it by clicking this link.

If you want to recall All Maths Formulas for Class 11, you can find it by clicking this link.

NCERT Solutions for Maths Class 12 Exercise 9.1

NCERT Solutions for Maths Class 12 Exercise 9.2

NCERT Solutions for Maths Class 12 Exercise 9.3

NCERT Solutions for Maths Class 12 Exercise 9.4

NCERT Solutions for Maths Class 12 Exercise 9.5

Find the general solution of the following differential equations in Q.1 to 12.

Maths Class 12 Ex 9.5 Question 1.

Solution:

The given equation is a linear differential equation of the form;

Here, P = 2 and Q = sin x

Now, the integrating factor (I.F.) is

Thus, the solution of the given differential equation is

This is the required general solution of the given differential equation.

Maths Class 12 Ex 9.5 Question 2.

Solution:

The given equation is a linear differential equation of the form;

Here, P = 3 and Q = e^-2x

Now, the integrating factor (I.F.) is

Thus, the solution of the given differential equation is

This is the required general solution of the given differential equation.

Maths Class 12 Ex 9.5 Question 3.

Solution:

The given equation is a linear differential equation of the form;

Here, P = 1/x and Q = x²

Now, the integrating factor (I.F.) is

Thus, the solution of the given differential equation is

This is the required general solution of the given differential equation.

Maths Class 12 Ex 9.5 Question 4.

Solution:
The given equation is a linear differential equation of the form;

Here, P = sec x and Q = tan x

Now, the integrating factor (I.F.) is

Thus, the solution of the given differential equation is

This is the required general solution of the given differential equation.

Maths Class 12 Ex 9.5 Question 5.

Solution:
The given differential equation can be written as dy/dx + (sec² x) y = tan x sec² x

This differential equation is of the form;

Here, P = sec² x and Q = tan x sec² x

Now, the integrating factor (I.F.) is

Thus, the solution of the given differential equation is

This is the required general solution of the given differential equation.

Maths Class 12 Ex 9.5 Question 6.

Solution:

The given differential equation can be written as dy/dx + 2y/x = x log x

This differential equation is of the form;

Here, P = 2/x and Q = x log x

Now, the integrating factor (I.F.) is

Thus, the solution of the given differential equation is

This is the required general solution of the given differential equation.

Maths Class 12 Ex 9.5 Question 7.

Solution:

The given differential equation is

This differential equation is of the form;

Here, P = 2/(x log x) and Q = 2/x²

Now, the integrating factor (I.F.) is

Thus, the solution of the given differential equation is

This is the required general solution of the given differential equation.

Maths Class 12 Ex 9.5 Question 8.

(1 + x²) dy + 2xy dx = cot x dx (x ≠ 0)

Solution:

The given differential equation is (1 + x²) dy + 2xy dx = cot x dx (x ≠ 0)

This differential equation is of the form

;

Here, P = 2x/(1 + x²) and Q = (cot x)/(1 + x²)

Thus, the solution of the given differential equation is

This is the required general solution of the given differential equation.

Maths Class 12 Ex 9.5 Question 9.

x dy/dx + y – x + xy cot x = 0 (x ≠ 0)

Solution:

The given differential equation is

This differential equation is of the form

;

Here, P = 1/x + cot x and Q = 1

Now, the integrating factor (I.F.) is

Thus, the solution of the given differential equation is

This is the required general solution of the given differential equation.

Maths Class 12 Ex 9.5 Question 10.

(x + y) dy/dx = 1

Solution:

The given differential equation is (x + y) dy/dx = 1

Or dx/dy – x = y

This differential equation is of the form dx/dy + Px = Q;
Here, P = –1 and Q = y

Now, the integrating factor (I.F.) is

Thus, the solution of the given differential equation is

This is the required general solution of the given differential equation.

Maths Class 12 Ex 9.5 Question 11.

y dx + (x – y²) dy = 0

Solution:

The given differential equation is y dx + (x – y²) dy = 0

Or dx/dy + x/y = y

This differential equation is of the form dx/dy + Px = Q;
Here, P = 1/y and Q = y

Now, the integrating factor (I.F.) is

Thus, the solution of the given differential equation is

This is the required general solution of the given differential equation.

Maths Class 12 Ex 9.5 Question 12.

(x + 3y²) dy/dx = y (y > 0)

Solution:

The given differential equation is

This differential equation is of the form dx/dy + Px = Q;

Here, P = –1/y and Q = 3y

Now, the integrating factor (I.F.) is

Thus, the solution of the given differential equation is

This is the required general solution of the given differential equation.

For each of the following Questions 13 to 15, find a particular solution satisfying the given condition:

Maths Class 12 Ex 9.5 Question 13.

Solution:

The given differential equation is

This differential equation is of the form;

Here, P = 2 tan x and Q = sin x

Thus, the solution of the given differential equation is

This is the required particular solution of the given differential equation.

Maths Class 12 Ex 9.5 Question 14.

Solution:

The given differential equation is

Thus, the solution of the given differential equation is

This is the required particular solution of the given differential equation.

Maths Class 12 Ex 9.5 Question 15.

Solution:

The given differential equation is

This differential equation is of the form;

Here, P = –3 cot x and Q = sin 2x

Thus, the solution of the given differential equation is

This is the required particular solution of the given differential equation.

Maths Class 12 Ex 9.5 Question 16.

Find the equation of the curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.

Solution:

The slope of the a tangent to a curve is given by dy/dx.

Now, from the given condition, we get

This differential equation is of the form;

Here, P = –1 and Q = x

Now, the integrating factor (I.F.) is

Thus, the solution of the given differential equation is

This is the required general solution of the given curve.

Maths Class 12 Ex 9.5 Question 17.

Find the equation of the curve passing through the point (0, 2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.

Solution:

The slope of the a tangent to a curve is given by dy/dx.

Now, from the given condition, we get
This differential equation is of the form;