Consider the equation $u_t = u_{xx}$, $0 < x < 1$, $t > 0$. Suppose $u(0,t) = 0 , u(1,t) = 0$. Suppose
$u(x,0) = -7 \sin(\pi x) - 4 \sin(2 \pi x) - 3 \sin(3 \pi x) + 1 \sin(4 \pi x)$

Fill in the constants in the solution:

$u(x,t) = {}$ $e^{-\pi^2t} \sin(\pi x) + {}$ $e^{-(2\pi)^2t} \sin(2 \pi x) + {}$ $e^{-(3\pi)^2t} \sin(3 \pi x) + {}$ $e^{-(4\pi)^2t} \sin(4 \pi x)$
help (numbers)