The problem involves finding the general solution of a first-order differential equation given by y'=(3*y^2-x^2)/(2*x-y). The equation is noted to be neither linear nor separable, and it has been checked for exactness, which was found to be not exact.
The discussion is ongoing, with participants exploring different methods and questioning the appropriateness of numerical solutions in the context of finding a general solution. There is no explicit consensus on the best approach yet.
Participants note that the problem requires a general solution, which raises questions about the validity of numerical methods in this context.
Thank you. But still, it is vague to how to approach the solution analytically.Dr. Courtney said: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 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?EM_Guy said: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