- #1

- 360

- 0

^{2}y' = (y

^{2}- xy)

which i changed to (y

^{2}- xy)dx + x

^{2}dy = 0

i then tried to solve using the substitution y = xv

dy = xdv + vdx

so ..

(x

^{2}v

^{2}) dx + x

^{2}(xdv + vdx) = 0

(v

^{2}- v) dx + xdv + vdx = 0

v

^{2}dx + xdv = 0

(1/x)dx + (1/v

^{2}) dv = 0

ln|x| + C - (1/v) = 0

y(x) = x/ln|x-A|, where A = e

^{C}

my answer is COMPLETELY different from what the solution is supposed to be according to wolfram. they got y(x) = 2x/(2Cx

^{2}+1)

what did i do wrong?