Determine whether the given function satisfies a Laplace equation.
-f(x, y) = cos(x) sin(-y)

Name: Determine whether the given function satisfies a Laplace equation. -f(x, y) = cos(x) sin(-y)
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Question

Quizplus · Accepted Answer

The Laplace equation is given by ∇^2f = 0, where ∇^2 is the Laplacian operator. For the given function f(x, y) = cos(x) sin(-y), the Laplacian is ∇^2f = ∂^2f/∂x^2 + ∂^2f/∂y^2 = -cos(x) sin(-y) - cos(x) sin(-y) ≠ 0. Therefore, the given function does not satisfy a Laplace equation.

Determine Whether the Given Function Satisfies a Laplace Equation