ok so i did this problem and checked in the back of my book and got it wrong..im hoping someone can show me the error of my work.
(y^2+yx)dx - x^2dy = 0
ok so there are a couple techniques that i can use to solve the problem...
1. almost exact
im going with homogeneous, because i think its a little easier to use and would require less steps.
so i make my substitution y= ux
therefore dy = udx +xdu
then after i make my substitution..
(u^2x^2 + ux^2) dx - x^2(udx + xdu)
after doing some algebra i got a final answer of
y = xC1 - x/ln|x|
C1 = 1/C
originally i got x/y = C - ln|x| i just flipped it and redefined my C, not sure if i can do this but it felt good? i dunno..lol thanks in advance.