What Is the Solution of the Following Initial Boundary Value $u(x, t)=e^{-16 \pi^{2} t} \sin \left(\frac{\pi x}{4}\right)$

Multiple Choice

What is the solution of the following initial boundary value problem?
4 = , u(0, t) = 0, u(2, t) = 0, u(x, 0) = sin(4?x)

A) $u(x, t) =e^{-16 \pi^{2} t} \sin \left(\frac{\pi x}{4}\right)$
B) $u(x, t) =e^{-64 \pi^{2} t} \sin (4 \pi t)$
C) $u(x, t) =\sum_{n=1}^{\infty} e^{-n^{2} \pi^{2} t} \sin \frac{n \pi x}{4}$
D) $u(x, t) =\sum_{n=1}^{\infty} e^{-n^{2} \pi^{2} /} \sin (4 n \pi x)$