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Finding the general solution to the DE

  1. Aug 3, 2010 #1
    1. The problem statement, all variables and given/known data

    (x^2)yy' = e^x

    2. Relevant equations

    general solution to the DE

    3. The attempt at a solution

    first i changed y' to dy/dx

    (x^2)y(dy/dx) = e^x

    then divided both members by x^2 and multiplied both members by dx

    ydy = (e^x)dx/(x^2)


    ydy = (x^-2)(e^x)dx

    how do i integrate (x^-2)(e^x)dx?
  2. jcsd
  3. Aug 3, 2010 #2
    ∫ex/x2 dx doesn't have an elementary antiderivative. Did you copy down the problem correctly?
  4. Aug 4, 2010 #3
    yeah. i copied it correctly..you may want to take a look at the problem statement..

    anyways, are there any methods to solve x-2exdx?

    or how do i solve this DE? it is the only problem in my homework that i couldnt slove.
  5. Aug 4, 2010 #4

    Gib Z

    User Avatar
    Homework Helper

    If you wanted you could integrate by parts to get:

    [tex]\int \frac{e^x}{x^2} dx = Ei (x) - \frac{e^x}{x} + C[/tex]

    where Ei(x) is the http://en.wikipedia.org/wiki/Exponential_integral" [Broken]. It doesn't really matter though, as Differential Equations are generally considered solved if your solution is a finite combination of known functions and integrals of known functions.
    Last edited by a moderator: May 4, 2017
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