Given u(x,y) = ф(3x-2y) (ф is an arbitrary function) find a PDE for u. Im just not sure how to start this question, any suggestions?
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Originally Posted by mel240 Given u(x,y) = ф(3x-2y) (ф is an arbitrary function) find a PDE for u. Im just not sure how to start this question, any suggestions? I guess you could do something like this $\displaystyle Au_{xx}+Bu_{yy}+Cu_{x}+Du_{y}+Fu=0$ A, B, C, D, E, F are constants.
Originally Posted by mel240 Given u(x,y) = ф(3x-2y) (ф is an arbitrary function) find a PDE for u. Im just not sure how to start this question, any suggestions? You'll notice that $\displaystyle \dfrac{\partial u}{\partial x} = 3\phi'(3x-2y)$ $\displaystyle \dfrac{\partial u}{\partial y} = -2\phi'(3x-2y)$ Now, can you think of a linear combination of these two to give you zero?
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