In each of the following differential equation show that it is homogeneous and solve it.
x² = x² + xy + y²

Question

In each of the following differential equation show that it is homogeneous and solve it.x2 = x2 + xy + y2

Philoid · Accepted Answer

⇒ 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:

⇒ tan ^- v = ln|x| + c

Resubstituting the value of y = vx we get

⇒ tan ^- (y/x) = ln|x| + c

Ans: tan ^- (y/x) = ln|x| + c