$\displaystyle u_{xxyy}+u_{xx}+u_{yy}=0$

Separation of variables

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

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- Dec 30th 2010, 01:32 PMdwsmithu_{xxyy}+u_{xx}+u_{yy}=0
$\displaystyle u_{xxyy}+u_{xx}+u_{yy}=0$

Separation of variables

With mixed partial derivatives, is it true that separation of variables wont work? - Dec 30th 2010, 04:35 PMSudharaka
Dear dwsmith,

Let $\displaystyle u(x,y)=f(x).g(x)$

$\displaystyle u_{xxyy}+u_{xx}+u_{yy}=0$

$\displaystyle f''(x).g''(y)+f''(x).g(y)+g''(y).f(x)=0$

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

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

So this partial differential equation is seperable.