## Rajasthan Board RBSE Class 12 Maths Chapter 12 Differential Equation Ex 12.6

**Solve the following differential equations :**

Question 1.

x^{2} ydx – (x^{3} + y^{3}) dy = 0

Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

So f(x,y) is homogeneous function.

∴ Given equation is homogeneous

Now y = vx …..(2)

Question 6.

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

Solution:

Question 7.

Solution:

Thus f (x, y) is homogeonous function.

∴ Given differential equation is homogeneous

Putting x = vy …..(2)

Question 8.

(3xy + y^{2}) dx + (x^{2} + xy) dy = 0

Solution:

Question 9.

Solution:

Question 10.

x (x-y) dy = y(x+y) dx

Solution: