Please help me solve this equation. I have tried many times but unable to solve it. $$e^y \left(\frac{dy}{dx} + 1\right) = e^x$$


closed as off-topic by Davide Giraudo, user91500, Michael Chernick, Dario, Magdiragdag Apr 21 '17 at 8:30

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Davide Giraudo, user91500, Michael Chernick, Dario, Magdiragdag
If this question can be reworded to fit the rules in the help center, please edit the question.

  • 2
    $\begingroup$ Hint: Try multiplying both sides by $e^x$ and then putting it in a form to test for an Exact Equation and then solving. $\endgroup$ – Moo Apr 20 '17 at 18:01
  • 3
    $\begingroup$ Many times... great... let's put all that hard work to use by putting the forward motion into the question statement so we can help you find your way. $\endgroup$ – rschwieb Apr 20 '17 at 18:02
  • $\begingroup$ @Dr.SonnhardGraubner shouldn't that be $y(x)=x - ln(2)$? $\endgroup$ – Χpẘ Apr 20 '17 at 18:26


If we put $$z=y+x $$

the equation becomes

$$z'e^z=e^{2x} $$

which gives $$e^z=\frac{1}{2}e^{2x}+C $$


$$y=z-x=\ln(\frac{1}{2}e^{2x}+C)-x $$


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