Odisha State Board Elements of Mathematics Class 12 Solutions CHSE Odisha Chapter 11 Differential Equations Ex 11(c) Textbook Exercise Questions and Answers.

## CHSE Odisha Class 12 Math Solutions Chapter 11 Differential Equations Exercise 11(c)

Find the solutions of the following differential equations:

Question 1.

(x + y) dy + (x – y) dx = 0

Solution:

Given equation can be written as

Question 2.

\(\frac{d y}{d x}\) = \(\frac{1}{2}\left(\frac{y}{x}+\frac{y^2}{x^2}\right)\)

Solution:

Question 3.

(x^{2} – y^{2}) dx + 2xy dy = 0

Solution:

Given equation can be written as

Question 4.

x\(\frac{d y}{d x}\) + \(\sqrt{x^2+y^2}\) = y

Solution:

Given equation can be written as

Question 5.

x (x + y) dy = (x^{2} + y^{2}) dx

Solution:

This is the required solution.

Question 6.

y^{2} + x^{2} \(\frac{d y}{d x}\) = xy \(\frac{d y}{d x}\)

Solution:

Given equation can be written as

This is the required solution.

Question 7.

x sin\(\frac{y}{x}\) dy = \(\left(y \sin \frac{y}{x}-x\right)\)dx

Solution:

Given equation can be written as

Question 8.

x dy – y dx= \(\sqrt{x^2+y^2}\) dx

Solution:

This is the required solution.

Question 9.

\(\frac{d y}{d x}\) = \(\frac{y-x+1}{y+x+5}\)

Solution:

Given equation is

This is the required solution.

Question 10.

(x – y) dy = (x + y + 1) dx

Solution:

Given equation can be written as

This is the required solution.

Question 11.

(x – y – 2) dx + (x – 2y – 3) dy = 0

Solution:

Given equation can be written as

This is the required solution.

Question 12.

\(\frac{d y}{d x}\) = \(\frac{3 x-7 y+7}{3 y-7 x-3}\)

Solution:

Given equation can be written as

This is the required solution.

Question 13.

(2x + y + 1) dx + (4x + 2y – 1) dy = 0

Solution:

Given equation can be written as

⇒ 2z + ln (z – 1) = 3x + C

⇒ 2 (2x + y) + ln (2x + y – 1 ) = 3x + C

⇒ (x + 2y) + ln (2x + y – 1 ) = C

This is the required solution.

Question 14.

(2x + 3y – 5)\(\frac{d y}{d x}\) + 3x + 2y – 5 = 0

Solution:

Given equation can be written as

Question 15.

(4x + 6y + 5) dx – (2x + 3y + 4) dy = 0

Solution:

Given equation can be written as

This is the required solution.