$\"\"$

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The function is $\"\"$ and differential equation is $\"\"$ .

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The function is $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The differential equation is $\"\"$ .

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Consider $\"\"$

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Substitute $\"\"$ and $\"\"$ in above expression.

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$\"\"$

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Therefore, $\"\"$ .

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$\"\"$

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