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Linear DE

  1. Jan 30, 2007 #1
    1. The problem statement, all variables and given/known data[/b]
    y'=4x–y+4; y(0)=8

    2. The attempt at a solution[/b]
    This is simply a first-order DE
    So:

    y'+y=4x+4
    P(x)=1
    Q(x)=4x+4
    p(x)=e^x
    So that ends up being:

    ye^x=(4xe^x+4e^x)dx

    Integration:
    ye^x=4xe^x-4e^x+4e^x

    ye^x=4xe^x
    divide by e^x
    y=4x+C
    y=4x+8


    However it tells me I'm wrong. either I'm very stupid or I'm going about this completely wrong.

    Thanks,
    Nate
     
  2. jcsd
  3. Jan 30, 2007 #2

    mjsd

    User Avatar
    Homework Helper

    note after the integration, you pick up a constant
    [tex]y e^x = 4 x e^x + C[/tex]
     
  4. Jan 30, 2007 #3
    Appreciate it!
     
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