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UnkleRhaukus
Can you check my DE solution please
\[\begin{align*} xy' &=y-xe^{y/x} \\ y' &=y/x-e^{y/x} \\ & &&\text{let } y/x=v \\ & &&y=xv \\ & &&y'=v+xv' \\ v+xv'&=v-e^v \\ xv'&=-e^v \\ {e^{-v}}{\dd v}&=-\frac{\dd x}x \\ \int{e^{-v}}{\dd v}&=-\int\frac{\dd x}x \\ -e^{-v}&=-\ln x+c \\ v&=-\ln(\ln x+c) \\ y/x&=-\ln(\ln x+c) \\ y(x)&=-x\ln(\ln x+c) \\ \end{align*}\]