$\"\"$

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The wave equation is $\"\"$ .

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The function is $\"\"$ .

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Apply partial derivative on each side with respect to $\"\"$ .

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$\"\"$

\

$\"\"$ .

\

Differentiate $\"\"$ partially with respect $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

The function is $\"\"$ .

\

Apply partial derivative on each side with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Differentiate $\"\"$ partially with respect $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Hence, the function $\"\"$ satisfies the wave equation. $\"\"$

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The function $\"\"$ satisfies the wave equation.