# Help me with this differential equation

$$xy'-y=x(1+e^{\frac{y}{x}})$$ Please give me a hint on how to solve this. If I'm not mistaken, this is a Bernoulli equation, but I can't seem to solve it using the substitution $z=y^{\frac{1}{1-a}}$. Using variation of constants also didn't help.

• @TIWARI You might mean $y=tx$. – Did Jun 25 '15 at 12:31

Try $u=\frac{y}{x}$. Then $y'=u'x+u$.
$y\backprime -\frac { y }{ x } =1+{ e }^{ \frac { y }{ x } }$ $\frac { y }{ x } =t$ , $\Rightarrow y=xt$ $\Rightarrow y\prime =t\prime x+t$ $\Rightarrow y\prime =t\prime x+t$ $\Rightarrow \int { \frac { dt }{ 1+{ e }^{ t } } =\int { \frac { dx }{ x } } }$
• May I suggest to forget completely the odd \backprime and \prime. – Did Jun 25 '15 at 12:31