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The function is $\"\"$ .

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Above equation satisfies the differential equation $\"\"$ .

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Find first and second derivatives of the function and substitute those results in above differential equation to find A and B.

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$\"\"$ .

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

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$\"\"$

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Derivative of the sine function: $\"\"$ .

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Derivative of the cosine function: $\"\"$ .

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$\"\"$

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

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$\"\"$

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Substitute the values of $\"\"$ and $\"\"$ in differential equation $\"\"$ .

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$\"\"$

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Compare $\"\"$ and $\"\"$ coefficients respectively.

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$\"\"$

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Solve above two equations to find $\"\"$ and $\"\"$ values.

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From equation $\"\"$ , we have $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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Thus, $\"\"$ and $\"\"$ .

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