Which of the following functions is the unique solution of the IBVP
$u_t = 4u_{xx}$, $0 < x < 2\pi$, $t > 0$
$u(0, t) = u(2\pi, t) = 0$, $t > 0$
$u(x, 0) = 2\sin x - 4\sin 4x$, $0 < x < 2\pi$.
Lütfen birini seçin:
A. $u(x, t) = 4\sin xe^{-4t} - 2\sin 4xe^{-32t}$
B. $u(x, t) = 2\sin xe^{-8t} - 4\sin 4xe^{-16t}$
C. $u(x, t) = 2\sin xe^{-4t} - 4\sin 4xe^{-16t}$
D. $u(x, t) = 4\sin xe^{-4t} - 2\sin 4xe^{-64t}$
E. $u(x, t) = 2\sin xe^{-4t} - 4\sin 4xe^{-64t}$
