Step 1:

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The function is $\"\"$ .

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

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$\"\"$

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Apply derivative of exponential function: $\"\"$ .

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$\"\"$

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Hence, $\"\"$ .

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Step 2:

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The function is $\"\"$ .

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

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$\"\"$

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Apply derivative of exponential function: $\"\"$ .

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$\"\"$

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Hence, $\"\"$ .

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

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$\"\"$

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The differential equation is $\"\"$

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Solution :

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The differential equation is $\"\"$