(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Heat Equation

3. 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?

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# ODE's for 2 space Heat equation

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