## Rajasthan Board RBSE Class 12 Maths Chapter 12 Differential Equation Ex 12.4

**Solve the following differential equations :**

Question 1.

(e^{y} + 1) cos x dx + e^{y} sin x dy = 0.

Solution:

Given equation is

Question 2.

(1 + x^{2}) dy = (1 + y^{2}) dx.

Solution:

Given

Question 3.

(x + 1) \(\frac { dy }{ dx } \) = 2xy

Solution:

Question 4.

Solution:

Question 5.

(sin x + cos x) dy + (cos x – sin x) dx = 0.

Solution:

Given (sin x + cos x) dy + (cos x – sin x) dx

Question 6.

Solution:

Question 7.

sec^{2} x tan y dy + sec^{2} y. tan x dx = 0.

Solution:

Given,

Question 8.

Solution:

Question 9.

(1 + cos x) dy = (1 – cosx) dx

Solution:

Question 10.

Solution: