MAT 205
MAT 205
Resit Exam - Page 4 of 6
5. Consider the following 1-D Heat equation,
$U_t = U_{xx}$,
$0 \le x \le 3$, $t > 0$
$U(0, t) = U(3, t) = 0$
$U(x, 0) = \sin(\pi x) - 2\sin(2\pi x)$
If the solution of the given heat equation is defined by $U(x, t)$ which is found by the method of separation
of variables then find the value of $U\left(\frac{1}{2}, 1\right)$
A) $e^{-x}$
B) $e^{-3x^2}$
C) $e^{-x^2}$
D) $2e^{-4x^2}$
E) $-2e^{-4x^2}$
