Question

how to solve x(xy+y+1)dy-ydx=0

Answer 1

The way it's written seems to suggest that it might be exact

Answer 2

it doesn't work on exact method

Answer 3

What are you solving for?

Answer 4

y

Answer 5

Hmmm let me think for a bit...\[
x(xy+y+1)dy-ydx=x(xy+y+1)y' dx-ydx
\]

Answer 6

\[
x(xy+y+1)dy=ydx \\
x(xy+y+1)y'=y \\
\frac{y'}{y} = \frac{1}{x(xy+y+1)} \\
(\ln(y))'=\frac{1}{x(xy+y+1)} \\
\ln(y) = \int \frac{1}{x(xy+y+1)} dx
\]