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Second order inhomogeneous differentiel equation.

  1. Aug 23, 2011 #1
    Hi everyone,

    1. The problem statement, all variables and given/known data

    I shall find the solution for the following differential equation:
    [tex] y''(x)+2y'(x)+y(x)=x^{2}+3 [/tex]



    2. Relevant equations
    -



    3. The attempt at a solution
    At first solved the homogenous equation and found the general solution for the homogenous as the following:

    [tex] y(x)=e^{-x}+xe^{-x}[/tex]

    Now I have to find an ansatz function I guess, but I don't know how to do this. I tried At³ but didn't work. Can someone help me?

    Thanks in advance
     
  2. jcsd
  3. Aug 23, 2011 #2
    Try
    [tex]y=ax^2+bx+c[/tex]
     
  4. Aug 23, 2011 #3
    Thanks, I guess that worked if I've done it correctly :smile:
     
  5. Aug 23, 2011 #4

    vela

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    It's easy enough to check. Just plug your solution into the LHS of the equation and see if you get the RHS when you simplify.
     
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