$\"\"$

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The equation is $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Verify the differential equation $\"\"$ and initial condition $\"\"$ correspond to the function $\"\"$ .

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Consider $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The initial condition $\"\"$ correspond to the function $\"\"$ .

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$\"\"$ is a particular solution to the differential equation.

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$\"\"$

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$\"\"$ is a particular solution to the differential equation.