Step 1:

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The function is $\"\"$ and differential equation is $\"\"$ .

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The function is $\"\"$ .

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Apply first derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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Use the derivative rule of exponential : $\"\"$

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$\"\"$

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Apply second derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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Step 2:

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The differential equation is $\"\"$ .

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Consider $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in above expression.

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$\"\"$

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Take out the common term in the above equation.

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$\"\"$

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Solve the equation $\"\"$ for r.

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Formula for solving a quadratic equation $\"\"$ : $\"\"$ .

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$\"\"$

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Therefore, The values of r that satisfy the differential equation are $\"\"$ .

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Solution :

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$\"\"$ .