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Solve ODE y''-y=e^{-t}

  1. Nov 26, 2011 #1
    1. The problem statement, all variables and given/known data
    Solve ODE
    [tex]y''-y=e^{-t}[/tex]

    [tex]y(0)=1, y'(0)=0[/tex]


    2. Relevant equations



    3. The attempt at a solution
    Homogenuous solution

    [tex]t^2-1=0[/tex]

    [tex]y=C_1e^t+C_2e^{-t}[/tex]

    From

    [tex]y(0)=1, y'(0)=0[/tex]

    [tex]y=\frac{1}{2}e^t+\frac{1}{2}e^{-t}[/tex]

    How from that get complete solution?
     
  2. jcsd
  3. Nov 26, 2011 #2

    hunt_mat

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    Re: Ode

    It's wrong. What you have to do it write:
    [tex]
    y=C_{1}e^{t}+C_{2}e^{-t}
    [/tex]
    and then find the particular integral, call it [itex]f(x)[/itex] say, and then apply the boundary condition to the function:
    [tex]
    y=C_{1}e^{t}+C_{2}e^{-t}+f(x)
    [/tex]
     
  4. Nov 26, 2011 #3
    Re: Ode

    How to find particular integral?
     
  5. Nov 26, 2011 #4

    hunt_mat

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    Re: Ode

    I would look for a function
    [tex]
    y=Ate^{-t}
    [/tex]
    and likewise.
     
  6. Nov 26, 2011 #5
    Re: Ode

    How do you know how to look for the function?
     
  7. Nov 26, 2011 #6
    Re: Ode

    How you choose form of particular solution?
     
  8. Nov 26, 2011 #7

    I like Serena

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