How to Solve a Non-Exact Differential Equation with an Integrating Factor?

[Ptopenny]

the problem is (x+x^4)dy+y(y^3-x^3)dx=0
well I know that this is not a separable equation, homogenous equation or an exact equation...so i try to solve it by treating it as a non exact DE by finding out the integrating factor...but the both IF come out in term of x and y which involve 2 variables where by IF must only has one variable...

 

[JJacquelin]

Hi !
The pattern of the ODE makes think to a change of variables : X=x^3 and Y=y^3, which leads to a Riccati ODE.

 

[Ptopenny]

thank god...u really help me very much :D :D