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Solving Initial Value Problem

  1. Sep 19, 2010 #1
    1. The problem statement, all variables and given/known data
    Solve the initial value problem (y+e^-y)y'=sinx subject to y(pi)=0

    2. Relevant equations

    3. The attempt at a solution
    I'm not quite sure what to do with this one. I've scanned through my book and could find no similar problems in what we've done so far. I tried to plug in dy/dx for y' and use separation of variables, but then I get stuck unable to solve for y after integrating. I cannot seem to find a way to set this one up to create an integrating factor either. If someone could nudge me in the right direction, I'd greatly appreciate it.
  2. jcsd
  3. Sep 19, 2010 #2


    Staff: Mentor

    I don't think you're going to be able to solve for y. I ended up with (1/2)y2 - e-y on one side, and a function of x on the other.

    Sometimes it's not possible to give the solution as an explicit function of x (ie., as y = f(x)), so the solution is given implicitly.

    As long as your equation satisfies the DE (you'll need to use implicit differentiation to solve for dy/dx) and initial condition, you're good.
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