Question

Can you check my DE solution please

Answer 1

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

Answer 2

Looks good to me.

Answer 3

yea looks pretty good

Answer 4

Thanks friends !