$\"\"$

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The differential equation is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Apply integral on each side.

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$\"\"$

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Apply power rule of integration: $\"\"$ .

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Apply formula: $\"\"$ .

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$\"\"$

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$\"\"$

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

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The initial condition is $\"\"$ .

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

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$\"\"$

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The particular solution is $\"\"$ . $\"\"$

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$\"\"$ .