Determine whether the given function satisfies a Laplace equation.
-$$f ( x , y , z ) = 5 x + 2 y ^ { 3 } z ^ { 2 }$$

Question

Quizplus · Accepted Answer

A Laplace equation is of the form $
abla ^ { 2 } f = 0$ which involves the Laplacian operator $
abla ^ { 2 } = \dfrac { \partial ^ { 2 } } { \partial x ^ { 2 } } + \dfrac { \partial ^ { 2 } } { \partial y ^ { 2 } } + \dfrac { \partial ^ { 2 } } { \partial z ^ { 2 } }$. Calculating the Laplacian of the given function, we get $
abla ^ { 2 } f = 12yz 
eq 0$. Therefore, the given function does not satisfy a Laplace equation.

Determine Whether the Given Function Satisfies a Laplace Equation f(x,y,z)=5x+2y3z2f ( x , y , z ) = 5 x + 2 y ^ { 3 } z ^ { 2 }f(x,y,z)=5x+2y3z2

Determine Whether the Given Function Satisfies a Laplace Equation $f ( x , y , z ) = 5 x + 2 y ^ { 3 } z ^ { 2 }$