The differential equation $\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } + \frac { \partial ^ { 2 } u } { \partial y ^ { 2 } } = u$ is
A) first order, linear, homogeneous
B) first order, linear, non-homogeneous
C) second order, nonlinear
D) second order, linear, homogeneous
E) second order, linear, non-homogeneous

Question

Quizplus · Accepted Answer

The given differential equation involves second derivatives with respect to both $x$ and $y$, making it a second-order equation. It is linear because $u$ and its derivatives appear to the first power without any products of $u$ and its derivatives. It is homogeneous because there is no term that is independent of $u$.

The Differential Equation ∂2u∂x2+∂2u∂y2=u\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } + \frac { \partial ^ { 2 } u } { \partial y ^ { 2 } } = u∂x2∂2u​+∂y2∂2u​=u

The Differential Equation $\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } + \frac { \partial ^ { 2 } u } { \partial y ^ { 2 } } = u$