Can you help me to find all solutions of differential equation $y'^2-(x+y)y'+xy=0$?
I wrote this equation as product of explicit equations:
$$(y'-x)(y'-y)=0$$
Then I found zeroes: $y'-x=0 \Longrightarrow y'=x \Longrightarrow y=\frac{x^2}2+C_1$
$y'=0$ I don't know what to do here. Maybe to solve as equation 'without $x$'? Am I doing this right?