First Order D.E (Not Linear, Exact, or Separable)

[AAO]

Homework Statement

What is the general solution of:

y'=(3*y^2-x^2)/(2*x-y)

Homework Equations

The Attempt at a Solution

This First Order equation is neither linear nor separable. I also have checked the Exact test, which turns to be Not Exact.

Any help regarding how this problem solution can be approached.

Thank you.

 

[Dr. Courtney]

http://www.wolframalpha.com/input/?i=solve+y'=(3*y^2-x^2)/(2*x-y)++for+y

Not a complete solution, but gives some insight and a way to double check your solution once you have it.

 

[EM_Guy]

Sounds like a problem that requires some kind of numerical method.

Maybe the Newton-Raphson method would work...

http://www.sosmath.com/calculus/diff/der07/der07.html
https://en.wikipedia.org/wiki/Newton's_method

 

[AAO]

http://www.wolframalpha.com/input/?i=solve+y'=(3*y^2-x^2)/(2*x-y)++for+y

Not a complete solution, but gives some insight and a way to double check your solution once you have it.

Thank you. But still, it is vague to how to approach the solution analytically.

 

[AAO]

Sounds like a problem that requires some kind of numerical method.

Maybe the Newton-Raphson method would work...

http://www.sosmath.com/calculus/diff/der07/der07.html
https://en.wikipedia.org/wiki/Newton's_method

Thank you for your comment. But the problem asks to find a general solution. So, even if it can be approached numerically, do you think this can be considered a general solution?