Differential Equations

  • Thread starter jofree87
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  • #1
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ex 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?

ex y dy/dx = e-y + e-2x-y

ex y dy/dx = e-y + e-2x e-y

ex y dy/dx = e-y ( 1 + e-2x )

ey y dy = e-x ( 1 + e-2x ) dx

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

ey (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.
 

Answers and Replies

  • #2
tiny-tim
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Hi jofree87! :smile:
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.

Looks fine. :smile:

(and i'm afraid you can't always check by differentiating! :wink:)
 

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