Determine whether each of the following functions is a solution of laplace's equation uxx + uyy = 0. (select all that apply.) u = e^(−x) cos(y) − e^(−y) cos(x) u = sin(x) cosh(y) + cos(x) sinh(y)

Answer with Step-by-step explanation:

We are given that Laplace's equation

We have to determine given function is  solution of given laplace's equation.

If a  function is solution of given Laplace's  equation then  it satisfy the solution.

1.

Differentiate w.r.t x

Then, we get

Again differentiate w.r.t x

Now differentiate u w.r.t y

Again differentiate w.r.t y

Substitute the values in given Laplace's equation

Hence, given function is a solution of given Laplace's equation.

2.

Differentiate w.r.t x

Again differentiate w.r.t x

Now, differentiate u w.r.t y

Again differentiate w.r.t y

Substitute the values then we get

Hence, given function is a solution of given Laplace's equation.