Friday, September 13, 2024
Home > CBSE Class 12 > NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6

# NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6

Hi Students, Welcome to Amans Maths Blogs (AMB). In this post, you will get the NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6.

The PDF books of NCERT Solutions for Class 12 are the first step towards the learning and understanding the each sections of Maths, Physics, Chemistry, Biology as it all help in engineering medical entrance exams. To solve it, you just need to click on download links of NCERT solutions for class 12.

CBSE Class 12th is an important school class in your life as you take some serious decision about your career. And out of all subjects, Maths is an important and core subjects. So CBSE NCERT Solutions for Class 12th Maths is major role in your exam preparation as it has detailed chapter wise solutions for all exercise. This NCERT Solutions can be downloaded in PDF file. The downloading link is given at last.

NCERT Solutions for Class 12 Maths are not only the solutions of Maths exercise but it builds your foundation of other important subjects. Getting knowledge of depth concept of CBSE Class 12th Maths like Algebra, Calculus, Trigonometry, Coordinate Geometry help you to understand the concept of Physics and Physical Chemistry.

As we know that all the schools affiliated from CBSE follow the NCERT books for all subjects. You can check the CBSE NCERT Syllabus. Thus, NCERT Solutions helps the students to solve the exercise questions as given in NCERT Books.

NCERT Solutions for class 12 is highly recommended by the experienced teacher for students who are going to appear in CBSE Class 12 and JEE Mains and Advanced and NEET level exams. Here You will get NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6 of all questions given in NCERT textbooks of class 12 in details with step by step process.

## NCERT Solutions for Class 12 Maths Differential Equations

For each of the differential equations given in Exercises 1 to 12, find the general solution:

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6: Ques No 1.

NCERT Solutions:

Given differential equation is .

This equation is a type of , where P = 2 and Q = sin x.

Now, the Integrating Factor (IF) is .

Thus, the solution of the given differential equation is .

Putting the values of IF and Q, we get

…(1)

Putting the value of I in equation (1), we get

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

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6: Ques No 2.

NCERT Solutions:

Given differential equation is .

This equation is a type of , where P = 3 and Q = e-2x.

Now, the Integrating Factor (IF) is .

Thus, the solution of the given differential equation is .

Putting the values of IF and Q, we get

…(1)

Now,

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

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6: Ques No 3.

NCERT Solutions:

Given differential equation is .

This equation is a type of , where P = 1/x and Q = x2.

Now, the Integrating Factor (IF) is .

Thus, the solution of the given differential equation is .

Putting the values of IF and Q, we get

…(1)

Now,

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

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6: Ques No 4.

NCERT Solutions:

Given differential equation is .

This equation is a type of , where P = sec x and Q = tan x.

Now, the Integrating Factor (IF) is .

Thus, the solution of the given differential equation is .

Putting the values of IF and Q, we get

…(1)

Now,

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

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6: Ques No 5.

NCERT Solutions:

Given differential equation is .

This equation is a type of , where P = sec2 x and Q = tan x sec2 x.

Now, the Integrating Factor (IF) is.

Thus, the solution of the given differential equation is .

Putting the values of IF and Q, we get

…(1)

Putting the value of I in equation (1), we get

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

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6: Ques No 6.

NCERT Solutions:

Given differential equation is.

This equation is a type of , where P = 2/x and Q = x log x .

Now, the Integrating Factor (IF) is .

Thus, the solution of the given differential equation is .

Putting the values of IF and Q, we get

…(1)

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

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6: Ques No 7.

NCERT Solutions:

Given differential equation is .

This equation is a type of , where P = 1/(x log x) and Q = 2/x2 .

Now, the Integrating Factor (IF) is.

Thus, the solution of the given differential equation is .

Putting the values of IF and Q, we get

…(1)

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

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6: Ques No 8.

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

NCERT Solutions:

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

This equation is a type of , where P = 2x/(1 + x2) and Q = (cot x)/(1 + x2) .

Since

Then, the Integrating Factor (IF) is .

Thus, the solution of the given differential equation is .

Putting the values of IF and Q, we get

…(1)

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

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6: Ques No 9.

NCERT Solutions:

Given differential equation is  .

This equation is a type of , where P = 1/x + cot x and Q = 1.

Then, the Integrating Factor (IF) is .

Thus, the solution of the given differential equation is .

Putting the values of IF and Q, we get

…(1)

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

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6: Ques No 10.

NCERT Solutions:

Given differential equation is . Or,

This equation is a type of , where P = -1 and Q = y.

Then, the Integrating Factor (IF) is .

Thus, the solution of the given differential equation is .

Putting the values of IF and Q, we get

…(1)

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

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6: Ques No 11.

y dx + (x – y2) dy = 0

NCERT Solutions:

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

This equation is a type of , where P = 1/y and Q = y.

Then, the Integrating Factor (IF) is .

Thus, the solution of the given differential equation is .

Putting the values of IF and Q, we get

…(1)

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

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6: Ques No 12.

NCERT Solutions:

Given differential equation is

This equation is a type of , where P = -1/y and Q = 3y.

Then, the Integrating Factor (IF) is .

Thus, the solution of the given differential equation is .

Putting the values of IF and Q, we get

…(1)

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

For each of the differential equations given in Exercises 13 to 15, find a particular solution satisfying the given condition:

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6: Ques No 13.

NCERT Solutions:

Given differential equation is .

This equation is a type of , where P = 2tan x and Q = sin x.

Since,

Then, the Integrating Factor (IF) is

Thus, the solution of the given differential equation is .

Putting the values of IF and Q, we get

…(1)

Since y = 0 at x = π/3, then

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

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6: Ques No 14.

NCERT Solutions:

Given differential equation is .

This equation is a type of , where .

Since,

Then, the Integrating Factor (IF) is

Thus, the solution of the given differential equation is .

Putting the values of IF and Q, we get

…(1)

Since y = 0 at x = 1, then

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

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6: Ques No 15.

NCERT Solutions:

Given differential equation is .

This equation is a type of , where P = -3cot x and Q = sin 2x.

Since,

Then, the Integrating Factor (IF) is

Thus, the solution of the given differential equation is .

Putting the values of IF and Q, we get

Since y = 2 at x = π/2, then

Hence,

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

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6: Ques No 16.

Find the equation of a 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.

NCERT Solutions:

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

Now, from the given information, we have

This equation is a type of , where P = -1 and Q = x.

Now, the Integrating Factor (IF) is

Thus, the solution of the given differential equation is .

Putting the values of IF and Q, we get

It is given that the curve passes through the origin (0, 0). We have x = 0, y = 0.

Hence,

This is the required particular solution of the given curve.

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6: Ques No 17.

Find the equation of a 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.

NCERT Solutions:

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

Now, from the given information, we have

This equation is a type of , where P = -1 and Q = x – 5.

Now, the Integrating Factor (IF) is

Thus, the solution of the given differential equation is .

Putting the values of IF and Q, we get

It is given that the curve passes through the origin (0, 2).

We have x = 0, y = 2. 2 = -0 + Ce0, then C = -2.

Hence,

This is the required particular solution of the given curve.

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6: Ques No 18.

The Integrating Factor of the differential equation is

(A) e–x

(B) e–y

(C) 1/x

(D) x

NCERT Solutions:

Given differential equation is or, .

This equation is a type of , where P = -1/x and Q = 2x.

Then, the Integrating Factor (IF) is

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.6: Ques No 19.

The Integrating Factor of the differential equation is

NCERT Solutions:

Given differential equation can be written as

This equation is a type of , where .

Then, the Integrating Factor (IF) is

AMAN RAJ
I am AMAN KUMAR VISHWAKARMA (in short you can say AMAN RAJ). I am Mathematics faculty for academic and competitive exams. For more details about me, kindly visit me on LinkedIn (Copy this URL and Search on Google): https://www.linkedin.com/in/ambipi/
error: Content is protected !!