Determine whether the given function satisfies a Laplace equation.
-$$f ( x , y ) = e ^ { 10 y } \sin 10 x$$

Question

Quizplus · Accepted Answer

The Laplace equation is satisfied if the second partial derivatives of the function with respect to x and y sum to zero. For $ f(x, y) = e^{10y} \sin 10x $, the second partial derivatives are $\frac{\partial^2 f}{\partial x^2} = -100 e^{10y} \sin 10x$ and $\frac{\partial^2 f}{\partial y^2} = 100 e^{10y} \sin 10x$, which sum to zero, satisfying the Laplace equation.

Determine Whether the Given Function Satisfies a Laplace Equation f(x,y)=e10ysin⁡10xf ( x , y ) = e ^ { 10 y } \sin 10 xf(x,y)=e10ysin10x

Determine Whether the Given Function Satisfies a Laplace Equation $f ( x , y ) = e ^ { 10 y } \sin 10 x$