NCERT Solutions for Class 12 Maths Differential Equations

Hi Students, Welcome to Amans Maths Blogs (AMB). In this post, you will get the NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.3.

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CBSE Class 12^th 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 12^th 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.

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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 9.3 of all questions given in NCERT textbooks of class 12 in details with step by step process. 

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 12^th Maths like Algebra, Calculus, Trigonometry, Coordinate Geometry help you to understand the concept of Physics and Physical Chemistry.

NCERT Solutions for Class 12 Maths Differential Equations

In each of the Exercises 1 to 5, form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.3: Ques No 1.

x/a + y/b = 1

NCERT Solutions:

Given equation is   

        …(1)

Differentiating (1) with respect to x, we get 

                                          …(2)

Differentiating (2) with respect to x, we get 

Thus, the differential equation of the given equation is y” = 0.

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.3: Ques No 2.

y² = a (b² – x²)

NCERT Solutions:

Given equation is  y² = a (b² – x²)        …(1)

Differentiating (1) with respect to x, we get 

2yy’ = a(– 2x) ⇒ yy’ = –ax                        …(2)

Differentiating (2) with respect to x, we get 

yy” + y’.y’ = –a                                      …(3)

Eliminating a between (2) and (3), we get  

yy’ = (yy” + y’.y’)x ⇒ yy’ = x(y’² + yy”)

Thus, the differential equation of the given equation is yy’ = x(y’² + yy”).

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.3: Ques No 3.

y = a e^3x + b e^{– 2x}

NCERT Solutions:

Given equation is  y = a e^3x + b e^{– 2x}        …(1)

Differentiating (1) with respect to x, we get 

y’ = a e^3x(3) + b e^{– 2x} (–2)                           …(2)

From (2) – 3 x (1), we get

y’ – 3y = –5be^–2x                                        …(3)

Differentiating (3) with respect to x, we get 

y” – 3y’ = –5be^–2x(–2)                                …(4)

From 3x(3) + (4), we get

y” – 3y’ + 2(y’ – 3y) = 0 ⇒ y” – y’ – 6y = 0 

Thus, the differential equation of the given equation is y” – y’ – 6y = 0.

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.3: Ques No 4.

y = e^2x (a + bx)

NCERT Solutions:

Given equation is  y = e^2x (a + bx)        …(1)

Differentiating (1) with respect to x, we get 

Again differentiating with respect to x, we get 

Thus, the differential equation of the given equation is y” – 4y’ + 4y = 0.

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.3: Ques No 5.

y = e^x (a cos x + b sin x)

NCERT Solutions:

Given equation is  y = e^x (a cos x + b sin x)        …(1)

⇒ e^-xy = (a cos x + b sin x)

Differentiating two times with respect to x, we get 

Thus, the differential equation of the given equation is y” – 2y’ + 2y = 0.

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.3: Ques No 6.

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

NCERT Solutions:

Thus, the differential equation of the family of circles touching the y-axis at origin is 2xyy’ + x² = y².

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.3: Ques No 7.

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

NCERT Solutions:

Thus, the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis is xy’ – 2y = 0.

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.3: Ques No 8.

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

NCERT Solutions:

Thus, the differential equation of the family of ellipses having foci on y-axis and centre at origin is x(y’² + yy”) – yy’ = 0.

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.3: Ques No 9.

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

NCERT Solutions:

Thus, the differential equation of the family of hyperbolas having foci on x-axis and centre at origin  is x(yy” + y’²) – yy’ = 0.

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.3: Ques No 10.

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

NCERT Solutions:

Thus, the differential equation of the family of circles having centre on y-axis and radius 3 units is x²(y’² + 1) = 9y’².

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.3: Ques No 11.

Which of the following differential equations has y = c₁ e^x + c₂ e^–x as the general solution?

NCERT Solutions:

Given equation is y = c₁ e^x + c₂ e^–x        …(1)

Differentiating (1) with respect to x, we get 

y’ = c₁ e^x – c₂ e^–x                                           …(2)

Differentiating (2) with respect to x, we get 

y” = c₁ e^x + c₂ e^–x ⇒ y” = y.

Thus, the differential equation of the given equation is y” = y.

NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.3: Ques No 12.

Which of the following differential equations has y = x as one of its particular solution?

NCERT Solutions:

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