The heat equation is
A) $\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } + \frac { \partial ^ { 2 } u } { \partial y ^ { 2 } } = 0$
B) $\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } + \frac { \partial u } { \partial y } = 0$
C) $\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } + \frac { \partial u } { \partial t } = 0$
D) $\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } - \frac { \partial u } { \partial t } = 0$
E) $\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } - \frac { \partial ^ { 2 } u } { \partial t ^ { 2 } } = 0$

Question

Quizplus · Accepted Answer

The correct form of the heat equation in one spatial dimension is $\frac{\partial^2 u}{\partial x^2} - \frac{\partial u}{\partial t} = 0$, which describes how the distribution of heat (u) in a given region changes over time.

The Heat Equation Is A) ∂2u∂x2+∂2u∂y2=0\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } + \frac { \partial ^ { 2 } u } { \partial y ^ { 2 } } = 0∂x2∂2u​+∂y2∂2u​=0

The Heat Equation Is
A) $\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } + \frac { \partial ^ { 2 } u } { \partial y ^ { 2 } } = 0$