Determine whether the given function satisfies a Laplace equation.
-$$f ( x , y ) = \frac { x ^ { 2 } } { y }$$

Question

Quizplus · Accepted Answer

A Laplace equation is of the form $\frac{\partial^2 f}{\partial x^2}+\frac{\partial^2 f}{\partial y^2}=0$. However, the given function does not satisfy this equation as taking partial derivatives with respect to $x$ and $y$ yield: $\frac{\partial^2 f}{\partial x^2}=0$ and $\frac{\partial^2 f}{\partial y^2}=-\frac{2x^2}{y^3}$, which are not equal to $0$. Therefore, the function does not satisfy a Laplace equation.

Determine Whether the Given Function Satisfies a Laplace Equation f(x,y)=x2yf ( x , y ) = \frac { x ^ { 2 } } { y }f(x,y)=yx2​

Determine Whether the Given Function Satisfies a Laplace Equation $f ( x , y ) = \frac { x ^ { 2 } } { y }$