Both functions are the solution to the given Laplace solution.
Given Laplace's equation:
- We must determine whether a given function is the solution to a given Laplace equation.
- If a function is a solution to a given Laplace's equation, it satisfies the solution.
(1)
Differentiate with respect to x as follows:
Differentiate with respect to y as follows:
Supplement the values in the given Laplace equation.
The given function in this case is the solution to the given Laplace equation.
(2)
Differentiate with respect to x as follows:
Differentiate with respect to y as follows:
Substitute the values to obtain:
The given function in this case is the solution to the given Laplace equation.
Therefore, both functions are the solution to the given Laplace solution.
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The correct question is given below:
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)