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## Homework Statement

## Homework Equations

## The Attempt at a Solution

I managed to do the first part of the question. But i'm not sure how to find u(x,t) with that initial condition.

The solution says; "since ##u(x,0) = \sum_{n=1}^\infty a_{n}\sin{(n\lambda x)}## Then it follows by linearity that ##u(x,t)=\sum_{n=1}^\infty a_{n}\sin{(n\lambda x)}e^{-n^2\lambda^{2}kt}##"

Could somebody please explain how the initial condition implies this. Thank you.