- #1
pondzo
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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.