General Formula using Miscellaneous Substitution

[asteg123]

I'm really stomped with this problem... i can't seem to get the answer...

anyway... here's the problem..

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

and i need to get the general solution...

SO, here's what i did...

I Let
u=x^3 and
du=3x^2dx

so what happens is

2udy-(y^3)dy= ydu

and that's where i got stuck...

i tried using
d(y/u)=(udy-ydu)/u^2

but i can't seem to get rid of the 2 in 2udy and it would be much of a problem if i did that...

could anyone help me??

 

[arildno]

Rewrite this diff.eq as:
$$y'=\frac{3\frac{y}{x}}{2-(\frac{y}{x})^{3}}\equiv{F}(\frac{y}{x}$$

I'm sure you have solved such problems previously.