- #1

billiards

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## Homework Statement

Solve: [tex]\frac{\partial H}{\partial t} = -4\kappa H^{2}[/tex]

With initial condition: [tex]H(0) = 1/L^{2}[/tex]

To find: [tex]H(t) = \frac{1}{4\kappa t + L^{2}}[/tex]

**2. The attempt at a solution**

I tried using Taylor series expansion such that:

[tex]H(t)\approx H(0)+t\frac{\partial H}{\partial t}(0)+...[/tex]

To first order this yielded: [tex]H(t)=\frac{L^{2}-4\kappa t}{L^{4}}[/tex]

This is wrong unless t and/or k equals zero. Therefore this is wrong, it is not the general solution. Please help if you can. Thanks.