e(adsbygoogle = window.adsbygoogle || []).push({}); ^{x}y dy/dx = e^{-y}+ e^{-2x-y}

Is this equation supposed to be solved through separation? I got an answer but it looks very messy. Can somebody check if I am doing this correctly?

e^{x}y dy/dx = e^{-y}+ e^{-2x-y}

e^{x}y dy/dx = e^{-y}+ e^{-2x}e^{-y}

e^{x}y dy/dx = e^{-y}( 1 + e^{-2x})

e^{y}y dy = e^{-x}( 1 + e^{-2x}) dx

Then Integrated by parts on both sides and got this solution:

e^{y}(y-1) = -e^{-x}- 1/3 e^{-3x}

Normally I would check it by plugging y and y' in to the differential equation but I dont know how to take the derivative of y in this particular solution.

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# Homework Help: Differential Equations

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