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Solving this ODE for an initial value problem

  1. Aug 26, 2014 #1
    1. The problem statement, all variables and given/known data
    [tex] x \frac{du}{dx} \ = \ (u-x)^3 + u[/tex]

    solve for u(x) and use [tex] u(1) \ = \ 10[/tex] to solve for u without a constant.

    2. Relevant equations

    The given hint is to let [itex]v=u-x[/itex]


    3. The attempt at a solution

    This equation is not separable and the book wants me to make it separable by a change of variables, i.e.

    [tex] u=v+x \ \ \text{and in replacing the original equation with the hint, I get} \frac{du}{dx} = \frac{v^3+u}{x} [/tex].

    From [tex]u=v+x, \ \text{I also know that} \frac{du}{dx} \ \text{is also equal to 1, so} \frac{v^3+u}{x} = 1 [/tex]

    But this gets rid of all the differentials and I need guidance on how to solve for u in terms of just x.
     
  2. jcsd
  3. Aug 26, 2014 #2

    LCKurtz

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    If ##u=v+x##, what is ##\frac {du}{dx}## in terms of ##v##? Also substitute for that ##u## that is left and show us what you get.
     
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