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Math Help - Particular and Complementary Solutions

  1. #1
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    Particular and Complementary Solutions

    u_x-u_y+u=1

    u_x-u_y+u=0

    u(x,y)=C_4\exp{[x\lambda+y(\lambda+1)]}+u_p(x,y)

    What method is used to solve for u_p(x,y)\mbox{?}

    I don't think the annihilator method can be used or I don't know how to use it with a PDE.
    Last edited by dwsmith; January 4th 2011 at 02:11 PM. Reason: added the or ...
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  2. #2
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    Quote Originally Posted by dwsmith View Post
    u_x-u_y+u=1

    u_x-u_y+u=0

    u(x,y)=C_4\exp{[x\lambda+y(\lambda+1)]}+u_p(x,y)

    What method is used to solve for u_p(x,y)\mbox{?}

    I don't think the annihilator method can be used or I don't know how to use it with a PDE.
    What about the method of undetermined coeffeints? The right hand side is a degree zero polynomial, so the particular solution must be a degree zero polynomial(a constant)
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    Quote Originally Posted by TheEmptySet View Post
    What about the method of undetermined coeffeints? The right hand side is a degree zero polynomial, so the particular solution must be a degree zero polynomial(a constant)
    I wasn't to sure about that either.

    If we let u_p=A, then u_{px}=0 \ u_{py}=0

    0-0+A=1

    u(x,y)=C_4\exp{[x\lambda+y(\lambda+1)]}+1

    So that is it?
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  4. #4
    Behold, the power of SARDINES!
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    yep, just plug it into the PDE to check that it satisfies the equation!
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