$\"\"$

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(a)

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The function is $\"\"$ .

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

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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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The differential equation is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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Therefore, $\"\"$ is not a solution of $\"\"$ .

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$\"\"$

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(b)

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The function is $\"\"$ .

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

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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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The differential equation is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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Therefore, $\"\"$ is not a solution of $\"\"$ .

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$\"\"$

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(c)

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The function is $\"\"$ .

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

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$\"\"$

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Apply product rule of derivative : $\"\"$ .

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Consider $\"\"$ and $\"\"$ .

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$\"\"$ and $\"\"$ .

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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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The differential equation is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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Cancel the common terms.

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$\"\"$

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Therefore, $\"\"$ is not a solution of $\"\"$ .

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$\"\"$

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(d)

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The function is $\"\"$ .

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

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$\"\"$

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Apply product rule of derivative : $\"\"$ .

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Consider $\"\"$ and $\"\"$ .

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$\"\"$ and $\"\"$ .

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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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The differential equation is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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Cancel the common terms.

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$\"\"$

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Therefore, $\"\"$ is a solution of $\"\"$ .

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The correct choice is $\"\"$ .

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$\"\"$

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The correct choice is $\"\"$ .