Originally Posted by

**^_^Engineer_Adam^_^** obtain the family of solutions

$\displaystyle x^2y' = 4x^2 + 7xy + 2y^2$

let

$\displaystyle y = vx$

$\displaystyle dy = vdx + xdv$

and after that i substitute and got a result of

$\displaystyle xdv + vdx = (4 + 7v + v^2)dx$

$\displaystyle \frac{dv}{4 + 6v + v^2}= \frac{dx}{x}$

i dont know if what i did is right .... im stuck with integrating the left part of this equation

thank you

edit

$\displaystyle xdv + vdx = (4 + 7v + 2v^2)dx$

i think i already know what's wrong with my soln

how do i delete this thread? thanks