Solving a first order differential equation (calculus 1)

[myeviltacos]

Homework Statement

dy/dx=y-e^-x

Homework Equations

none

The Attempt at a Solution

According to Wolfram Alpha the solution is y = ce^x+.5e^-x . I tried multiple approaches, but I cannot obtain this answer. I can't figure out what step 1 is.

I tried factoring out e^-x from the right side of the equation, but I couldn't go anywhere from there, and factoring out y did not work either.

 

[Char. Limit]

First rearrange it to dy/dx + p(x) y = q(x), where p(x) and q(x) are arbitrary functions. Then find an integrating factor.

 

[myeviltacos]

First rearrange it to dy/dx + p(x) y = q(x), where p(x) and q(x) are arbitrary functions. Then find an integrating factor.

Oh wow, thanks for your response. I solved it. :)