Question

Find the general solution for EQ:
(x^2+3xy+y^2)dx-(x^2)dy=0

Answer 1

First solve for dy/dx and then integrate.

Answer 2

Thanks, i know I need to find an integrating factor, but how do i find it?

Answer 3

the only method i know, kinda konw, is seperation of variables....

Answer 4

> (x^2+3xy+y^2)dx = (x^2)dy........(1)
>(1)/x^2 => [1+3(y/x)+(y/x)^2 = dy/dx
> let y/x=v,then dy/dx=v+x(dv/dx)
>so above equation reduces to 1+3v+v^2 = v+x(dv/dx)
>1+2v+v^2 = x(dv/dx)
>(1/x) dx =(1/(1+v)^2)dv,then integrate both sides