Solve the boundary value problem $\displaystyle x''(t) + 3 x(t) = \sum_{n=1}^\infty \frac{6}{n^2} \sin( n \pi t)$ with $x(0) = 0 , x(1) = 0$ .

The solution is $\displaystyle x(t) = \sum_{n=1}^\infty b_n \sin (n \pi t)$ where
$b_n = {}$

Write out the first 3 harmonics of this series:


help (formulas)