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Easy ODE

  1. Apr 22, 2010 #1
    [tex] y'= \frac{y}{1+e^x}+e^{-x} [/tex]

    It's an easy first order linear inhomogenous eq. I solved it by hand with the formula that one can find anywhere AND with Mathematica, but when I take the derivative to check the solution it comes out wrong and it's freaking me out. Can anyone here post just the plain solution?
  2. jcsd
  3. Apr 23, 2010 #2
    Just use the method of variating the constant, and you get:

    <math>y(x) = C\frac{e^x}{1+e^x}-\frac{2+e^{-x}}{2(1+e^x)} </math>
  4. Apr 23, 2010 #3
    <tex>y(x) = C\frac{e^x}{1+e^x}-\frac{2+e^{-x}}{2(1+e^x)} </tex>
  5. Apr 23, 2010 #4
    oops used the wrong brackets for math mode, so here it is:

    [tex]y(x) = C\frac{e^x}{1+e^x}-\frac{2+e^{-x}}{2(1+e^x)} [/tex]
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