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Solving Partial Differential Equations

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1. Solve

u(0,t) = u(,t) =0

u(x,0) = xsinx ,

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1. Solve

u(0,t) = u(,t) =0

u(x,0) = xsinx ,

We start by setting the function u(x,t) as a product of a single-variable functions:

Therefore the partial derivatives become:

Plugging it back into the equation, one obtains:

Dividing by separates the equation:

Since both sides are totally independent (each is a function of an ...

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