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Homework Help: Reduction of order ODE

  1. Apr 4, 2010 #1
    1. The problem statement, all variables and given/known data

    Solve:
    [tex]
    y'' -y' e^{y'^2-y^2} = 0
    [/tex]

    y(0) = 1
    y'(0) = 0

    2. Relevant equations



    3. The attempt at a solution

    No idea how to use it.
    If I use the substituion y' = p, and y'' = p'p I need to integrate [itex]e^{y^2}[/itex] which is unintegratable. What should I do?
     
  2. jcsd
  3. Apr 4, 2010 #2

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    According to your DE and initial conditions, what is [itex]y''(0)[/itex]? How about [tex]\left.\frac{d^n y}{dx^n}\right|_{x=0}[/tex] ? What might you expect the solution to be if all the derivatives are zero at some point? Can you prove that is the only solution?
     
  4. Apr 4, 2010 #3
    I get what you're trying to say - that the solution is y=1.
    I don't know how to prove it though.
     
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