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