Question

Determine whether the following functions are solutions of Laplace’s equation
z = e^x cos y

Answer 1

\[\frac{∂^{2}z}{∂x^{2}}+\frac{∂^{2}z}{∂y^{2}}=0\]

Answer 2

lol, you cant find "∂" here, try google

Answer 3

I think i've found it myself,
\[\frac{∂z}{∂x}=e^{x} \cos~y,~~ \frac{∂^{2}z}{∂x^{2}}=e^{x} \cos~y\]
\[\frac{∂z}{∂y}=-e^{x} \sin~y,~~ \frac{∂^{2}z}{∂y^{2}}=-e^{x} \cos~y\]
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Then,
\[\frac{∂^{2}z}{∂x^{2}}+\frac{∂^{2}z}{∂y^{2}}=0\]
:D

Answer 4

well, it satisfies the equation ... but, you know the function before hand ... and thats not the general clase.
first you have differential equation and then you find the solution. well, anyway good luck