$\"\"$

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The diffrental 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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Diffrentiate with respect to $\"\"$ .

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$\"\"$

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The first derivative is $\"\"$ .

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Diffrentiate with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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

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$\"\"$

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Therefore, the differntial equation condition is satisfied.

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

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$\"\"$

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Consider the general solution $\"\"$ .

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Substiute $\"\"$ 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 $\"\"$ .