In each of the following differential equation show that it is homogeneous and solve it.

Question

In each of the following differential equation show that it is homogeneous and solve it. x 2 dy + y(x + y)dx = 0

Philoid · Accepted Answer

x²dy + y(x + y)dx = 0

⇒ the given differential equation is a homogenous equation.

The solution of the given differential equation is :

Put y = vx

Integrating both the sides we get:

Resubstituting the value of y = vx we get

⇒ x²y = c²(y + 2x)

Ans: x²y = c²(y + 2x)