You started out just fine. With both substitutions and you get a horrendous integration that looks like
or
Both integrals are pretty nasty. Not really sure what to do from here. Ideas, anyone else?
ok so here is the problem...
(x^2+ xy)dx - (2xy + y^2)dy = 0 let y = ux
ok the problem seems easy enough... if y = ux then dy = udx + xdu
so now im ready to substitute...
when i solved it i got something like
ln|x| = (2u^2 + u)/(-u^3-2u^2+u+1)
so where did i go wrong...
(x^2 +ux^2)dx - [(2ux^2 + (ux)^2)](udx + xdu) from here i used algebra to simplify?
thanks in advance...
Check the numerator. It should be:
Fernando Revilla
Edited: Sorry, I didn't see Ackbeet's post
Mathematica Version 4 and WolframAlpha won't integrate it, either. You're not alone! You're probably good if you reduce the DE to integrals - but that's about as far as you can go with this one, I think, unless there's a clever substitution or an integrating factor to get the equation exact. It's not linear or Bernoulli in x or y.