# 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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**NCERT Solutions for Class 12 Maths Differential Equations Exercise 9.3*** 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

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**CBSE Class 12**^{th}Maths## 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.**

y^{2} = a (b^{2} – x^{2})

**NCERT Solutions:**

Given equation is y^{2} = a (b^{2} – x^{2}) …(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^{-x}y = (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’ + x^{2} = y^{2}.

**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 x^{2}(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 = c_{1} e^{x} + c_{2} e^{–x} as the general solution?

**NCERT Solutions:**

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

Differentiating (1) with respect to x, we get

y’ = c_{1} e^{x} – c_{2} e^{–x} …(2)

Differentiating (2) with respect to x, we get

y” = c_{1} e^{x} + c_{2} 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:**