Results 1 to 2 of 2

Math Help - u_{xxyy}+u_{xx}+u_{yy}=0

  1. #1
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5

    u_{xxyy}+u_{xx}+u_{yy}=0

    u_{xxyy}+u_{xx}+u_{yy}=0

    Separation of variables

    With mixed partial derivatives, is it true that separation of variables wont work?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Dec 2009
    From
    1111
    Posts
    872
    Thanks
    3
    Quote Originally Posted by dwsmith View Post
    u_{xxyy}+u_{xx}+u_{yy}=0

    Separation of variables

    With mixed partial derivatives, is it true that separation of variables wont work?
    Dear dwsmith,

    Let u(x,y)=f(x).g(x)

    u_{xxyy}+u_{xx}+u_{yy}=0

    f''(x).g''(y)+f''(x).g(y)+g''(y).f(x)=0

    f''(x)\{g''(y)+g(y)\}=-g''(y).f(x)

    \dfrac{f''(x)}{f(x)}=-\dfrac{g''(y)}{g''(y)+g(y)}

    So this partial differential equation is seperable.
    Follow Math Help Forum on Facebook and Google+


/mathhelpforum @mathhelpforum