In the previous problem, the solution for $U ( \alpha , t )$ is
A) $U = u _ { 0 } \left( 1 + e ^ { - k \alpha ^ { 2 } t } \right) / \alpha$
B) $U = u _ { 0 } \left( 1 - e ^ { - k \alpha ^ { 2 } t } \right) / \alpha$
C) $U = u _ { 0 } \left( 1 - e ^ { k \alpha ^ { 2 } t } \right) / \alpha$
D) $U = u _ { 0 } \left( 1 - e ^ { k \alpha ^ { 2 } t } \right)$
E) $U = u _ { 0 } \left( 1 + e ^ { - k \alpha ^ { 2 } t } \right)$

Question

Quizplus · Accepted Answer

The correct solution involves a decay term $e^{-k\alpha^2t}$, which decreases over time, and the division by $\alpha$ to ensure the solution's dimensionality is consistent.

In the Previous Problem, the Solution For U(α,t)U ( \alpha , t )U(α,t)

In the Previous Problem, the Solution For $U ( \alpha , t )$