$\"\"$

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The substitution is

\

The expression for velocity of falling object is $\"\"$ .

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Differentiate on each side with respect to $\"\"$ ..

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$\"\"$

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$\"\"$ .

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Logistic differential equation is $\"\"$ .

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Thus, $\"\"$

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$\"\"$

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Replace $\"\"$ in the expression. \ \

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$\"\"$

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$\"\"$ .

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$\"\"$

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(b)

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Consider $\"\"$ .

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Solution for the linear differential equation $\"\"$ is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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From 9.4.7 $\"\"$ .

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Compare the both equations, here $\"\"$ .

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$\"\"$

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(a) $\"\"$ .

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(b) $\"\"$ .