$\"\"$

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The differential equation is $\"\"$ .

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The general solution is $\"\"$ .

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Initial conditions:

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

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Consider $\"\"$ .

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Differentiate with respect to $\"\"$ .

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$\"\"$

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The first derivative is $\"\"$ .

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Differentiate with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute the values of $\"\"$ in $\"\"$ .

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$\"\"$

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Therefore, the differential equation condition is satisfied.

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To find out the particular solution substitute $\"\"$ in $\"\"$ .

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$\"\"$

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Consider the general solution $\"\"$ .

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Substitute $\"\"$ in the general solution.

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$\"\"$

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The particular solution is $\"\"$ .

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$\"\"$

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Quotient rule of logarithm: $\"\"$ .

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$\"\"$ .

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$\"\"$

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The particular solution is $\"\"$ .