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Forums
Mathematics
Differential Equations
Separation of variables possible in this problem?
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[QUOTE="jasonRF, post: 6369431, member: 192203"] Yes, something more clever will be required because presence of the ##u_{xy}## term as well as the nonhomogeneous term ##k## mean that straightforward separation of variables will not work. Getting rid of ##k## is easy: let ##u(x,y) = f(x,y) - k## and the equation for ##f## is homogeneous. Dealing with the ##u_{xy}## term isn't so easy, but sometimes a trick applies. First [I]try[/I] separation of variables so you have an equation with terms such as ## \frac{X^{\prime\prime}(x)}{X(x)}##, etc. Then, differentiate that equation with respect to ##y##; the resulting equation might be separable. Of course, even if the equation is separable you still need separable boundary conditions along curves of constant ##x## and ##y## in order for separation of variables to apply to your problem. jason [/QUOTE]
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Mathematics
Differential Equations
Separation of variables possible in this problem?
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