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A Can you solve (a-bx)y'+(c-dx)y-e=0 with a,b,c,d,e constants?

  1. Feb 17, 2017 #1
    I'm having trouble solving the differential equation (a-bx)y'+(c-dx)y-e=0 with a,b,c,d,e constants.
    I tried laplace transforming it, but then I end up with yet another differential equation in the laplace domain because of the xy and xy' terms.
  2. jcsd
  3. Feb 17, 2017 #2

    Simon Bridge

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    So what methods have you ruled out?

    You really want to avoid using "d" as a constant label in differential equations.

    The DE is 1st order, linear, and has form:
    y' + p(x)y = q(x) if you put p = (c-dx)/(a-bx) and q=e/(a-bx)

    More generally: f(x)y' + g(x)y = e

    Have you looked for an integrating factor? - watch for funny integrals like the gamma function.
  4. Feb 17, 2017 #3
    Thanks a lot! That works, but indeed I end up with a funny integral that does not have an analytical solution. I was hoping for an elegant solution, but I'll have to rely on my computer then.
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