24 24 The two-dimensional Laplace equation, 2+2=0, describes potentials and steady-state temperature distributions in a plane. Show that the following function satisfies the two-dimensional Laplace equati dx dy f(x,y) = 5x-9y-6

The two-dimensional Laplace equation is given by d^2f/dx^2 + d^2f/dy^2 = 0, where f(x, y) is a function of two independent variables x and y. This equation is used to describe the potentials and steady-state temperature distributions in a plane.

To show that the function f(x, y) = 5x - 9y - 6 satisfies the two-dimensional Laplace equation, we need to take the second partial derivatives of f with respect to x and y, and then add them together.

The first partial derivative of f with respect to x is given by ∂f/∂x = 5, and the second partial derivative of f with respect to x is given by ∂^2f/∂x^2 = 0. This is because the second derivative of a linear function with respect to its independent variable is always zero.