In the Previous Three Problems, the Solution For $u ( x , t )$

Multiple Choice

In the previous three problems, the solution for $u ( x , t )$ is

A) $\int _ { - \infty } ^ { \infty } \left[ e ^ { - i \alpha x } e ^ { k at } / \left( 1 + \alpha ^ { 2 } \right) \right] d \alpha / ( 2 \pi )$
B) $\int _ { - \infty } ^ { \infty } \left[ e ^ { - i \alpha x } e ^ { - k \alpha ^ { 2 } t } / \left( 1 + \alpha ^ { 2 } \right) \right] d \alpha / \pi$
C) $\int _ { - \infty } ^ { \infty } \left[ e ^ { - i \alpha \alpha } e ^ { k \alpha t } / \left( 1 + \alpha ^ { 2 } \right) \right] d \alpha / \pi$
D) $\int _ { - \infty } ^ { \infty } \left[ e ^ { - i \alpha x } e ^ { - k \alpha t } / \left( 1 + \alpha ^ { 2 } \right) \right] d \alpha / \pi$
E) $\int _ { - \infty } ^ { \infty } \left[ e ^ { - i \alpha \alpha } e ^ { k \alpha ^ { 2 } t } / \left( 1 + \alpha ^ { 2 } \right) \right] d \alpha / ( 2 \pi )$