RBSE Solutions for Class 12 Maths Chapter 12 Differential Equation Ex 12.6

RBSE Solutions for Class 12 Maths Chapter 12 Differential Equation Ex 12.6

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

Solve the following differential equations :

Question 1.
x² ydx – (x³ + y³) 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.
(x² +y²) 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 + y²) dx + (x² + xy) dy = 0
Solution:

Question 9.

Solution:

Question 10.
x (x-y) dy = y(x+y) dx
Solution: