## Rajasthan Board RBSE Class 12 Maths Chapter 12 Differential Equation Ex 12.7

**Solve the following differential equations :**

Question 1.

Solution:

h and k are such that

3h + 2k – 5 = 0 and 2h + 3k – 5 = 0

Putting these values in equation

h = 1 ,k = 1

This is homogeneous equation

Question 2.

Solution:

Question 3.

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

Solution:

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

Question 4.

Solution:

∴ Integrating

x + C = – 2v – 2 log (1 – v)

or x + C + 2(x + y) + 2 log (1 – x – y) = 0

[∵ v = x + y]

or 3x + 2y + 2 log (1 – x – y) + C = 0,

This is required solution.

Question 5.

Solution: