Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Im clueless on how to solve the following question...

$xe^y\frac {dy}{dx} = e^y +1$

What i've done is...

$\frac {dy}{dx} = \frac 1x + \frac {1}{xe^e}; \frac {dy}{dx} - \frac {1}{xe^e} = \frac 1x $

Find the integrating factor..

$v(x) = e^{P(x)}; where P(x) = \int p(x)dx \Rightarrow P(x) = \int \frac 1x dx = ln|x| \\v(x) = e^{P(x)} = e^{ln|x|} = x; \\ y = \frac {1}{v(x)} \int v(x)q(x) dx = \frac 1x \int {x}{\frac 1x} dx = 1+c$

I know I made a mistake somewhere. Would someone advice me on this??

share|cite|improve this question
solve rather $x\,dz/dx=z+1$ and then set $z=e^y$ – user8268 Nov 13 '12 at 9:50
up vote 2 down vote accepted

You have $xe^y\frac{dy}{dx}=e^y+1$, so, by dividing both sides by $x$ and by $e^y+1$, we get $$\begin{align*}\frac{e^y}{e^y+1}\frac{dy}{dx}=\frac1x\hspace{5pt}&\Rightarrow \hspace{5pt}\frac{e^y}{e^y+1}dy=\frac1xdx\hspace{5pt}\Rightarrow \hspace{5pt}\int\frac{e^y}{e^y+1}dy=\int\frac1xdx \\ &\Rightarrow\hspace{5pt}\ln(e^y+1)=\ln (C|x|)\hspace{5pt}\Rightarrow \hspace{5pt}e^y+1=C|x|\end{align*}$$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.