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

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

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    $\begingroup$ 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
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    $\begingroup$ 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
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hint

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

the equation becomes

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

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

and

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

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