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This is the problem:

For the differential equation

$y'=$exp$(x−y)$

find the solution for the initial value problem $y(0)=0$.

I tried to plug in 0 into the equation, which lead me nowhere - $0=exp(x)$. What am I doing wrong, and how do I get the correct answer? Thanks.

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  • $\begingroup$ Hint: $y'\, e^y=e^x $. $\endgroup$ – Pocho la pantera Sep 4 '13 at 0:52
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The equation can be written as $$ e^y \,dy=e^x \, dx $$ Integrating we obtain $$ e^y=e^x +c $$ So, if $y(0)=0$ then $c=0$. Therefore $y=x$.

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  • $\begingroup$ Oh, so you have to mess around with the $e$'s to get to the answer. That definitely helps a lot, thank you. $\endgroup$ – user91971 Sep 4 '13 at 6:16

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