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beetle2
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Homework Statement
The Heat equation in two space is
[itex]\alpha ^2 \left[\frac{\partial ^2u}{\partial x^2}+\frac{\partial ^2u}{\partial y^2} \right]=\frac{\partial u}{\partial t}[/itex]
Assuming separation solution of the form [itex]u(x,y,t)=F(x)G(y)H(t)[/itex] find ordinary differential equations satisfied by F,G and H.
Homework Equations
Heat Equation
The Attempt at a Solution
Because we can assume [itex]u(x,y,t)=F(x)G(y)H(t)[/itex]
Is the first step that we require that
[itex]\alpha^2\frac{F''}{F}+\alpha^2\frac{G''}{G}=\frac{H'}{H}[/itex]
therefore we need to solve
[itex]F''+\frac{k}{\alpha^2}F+G''+\frac{k}{\alpha^2}G=0[/itex]
and
[itex]H'-kH=0[/itex]
Is this right so far?