Question

\[xy'=y-xe^{y/x}\]

Answer 1

\[xy'=y-xe^{y/x}\]\[y'=y/x - e^{y/x}\]
let \[y=vx\]\[ y' =xv'+v\]
\[xv'+v=v-e^v\]\[v'=-{1 \over x} e^{v}\]
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Answer 2

...\[e^{-v}dv=-{1 \over x} dx\]\[ \int e^{-v}dv=-\int{1 \over x} dx\]\[-e^v = ln(x)+c\]
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Answer 3

\[-e^{y/x} = ln(x) + c\]

Answer 4

now what do i do?