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Finding basic solutions to a PDE?

  1. Feb 16, 2010 #1
    Finding basic solutions to a PDE??

    So the problem is:
    x_o=0
    [tex]\varphi''[/tex] + 4[tex]\varphi'[/tex] + [tex]\lambda[/tex][tex]\varphi[/tex]=0

    which satisfies [tex]\varphi(0)[/tex]=3 and [tex]\varphi'(0)[/tex]=-1

    I really dont even know where to start, I think its like an ODE right where we assume a solution, usually sin or an exponential and plug it in for each psi and its derivatives, find roots and plud back into a genral solution and use BC to find constants. In the text though, they give psi as a linear combo of psi 1 and psi 2 with some coefficients in front. The answer they give is an exponential multiplied by a sin term and a cos term for psi 1 and an exponential multiplied by a sin term.
    thanks for any help all
     
  2. jcsd
  3. Feb 17, 2010 #2
    Re: Finding basic solutions to a PDE??

    the equation is linear with constant coefficients. Try
    [tex]\phi=Ae^{st}[/tex]
    which will give you a condition on s, for which you get two solutions, [tex]s_{1},s_{2}[/tex]. Then plug
    [tex]\phi=Ae^{s_{1}t}+Be^{s_{2}t}[/tex]
    into the boundary conditions to get the coefficients
     
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