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Derivative Problem

  1. Nov 1, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the constants A, B, and C such that the function [tex]y=Ax^{2}+Bx+C[/tex] satisfies the differential equation [tex]y^{''}+y^{'}-2y=x^{2}[/tex].

    3. The attempt at a solution
    I know that [tex]y^{''}+y^{'}-2Ax^{2}-2Bx-2C=x^{2}[/tex] and that [tex]y^{'}=2Ax+B[/tex] and [tex]y^{''}=2A[/tex], but I'm really stuck at this point. Any help would be appreciated.
  2. jcsd
  3. Nov 2, 2009 #2


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    Homework Helper

    almost there, substitute in for y & y'

    each power of x will give you an equation that must be solved for the solution to satisfy teh differential equation

    eg. the co-efficients of x^1 must add up to zero
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