$\"\"$

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

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

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Consider $\"\"$ .

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Diffrentiate with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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The first derivative is $\"\"$ .

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$\"\"$

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$\"\"$

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Consider the general solution $\"\"$ .

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Substitute the values in the general solution.

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

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$\"\"$

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Consider the first derivative $\"\"$ .

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$\"\"$

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$\"\"$

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Solve the equations $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute the value $\"\"$ in equation $\"\"$ .

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$\"\"$

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

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$\"\"$ .

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$\"\"$

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The particular solution is $\"\"$ .