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Math Help - u_{xxx}+u_x=0

  1. #1
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    u_{xxx}+u_x=0

    Find the general solution of u(x,y,z) of

    u_{xxx}+u_x=0

    Can I use this method m^3+m=0 for PDE?

    Thanks.

    m(m^2+1)=0\Rightarrow m_1=0 \ \ m_2=\mathbf{i} \ \ m_3=-\mathbf{i}

    u(x,y,z)=f(y,z)e^{0}+g(y,z)e^{x\mathbf{i}}\Rightar  row u(x,y,z)=f(y,z)+g(y,z)e^{x\mathbf{i}}

    Pickslides I just read your other post and the answer is yes I am presuming.
    Last edited by dwsmith; December 23rd 2010 at 05:31 PM. Reason: Pulled out too many ms.
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  2. #2
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    Quote Originally Posted by dwsmith View Post
     u(x,y,z)=f(y,z)+g(y,z)e^{x\mathbf{i}}

    Pickslides I just read your other post and the answer is yes I am presuming.
    Does it satisfy \displaystyle u_{xxx}+u_x=0 ?
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  3. #3
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    Quote Originally Posted by pickslides View Post
    Does it satisfy \displaystyle u_{xxx}+u_x=0 ?
    Yes, u_x=\mathbf{i}e^{x\mathbf{i}}g(y,z) \ , \ u_{xxx}=-\mathbf{i}e^{x\mathbf{i}}g(y,z)

    -\mathbf{i}e^{x\mathbf{i}}g(y,z)+\mathbf{i}e^{x\mat  hbf{i}}g(y,z)=0
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