Step 1:

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The differential equation is $\"\"$ .

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$\"\"$

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Apply integration on each side.

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$\"\"$

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$\"\"$

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Apply long division to simplify the integral.

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$\"\"$

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Apply integration sum and difference formula $\"\"$ .

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$\"\"$

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$\"\"$

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Partial fraction decomposition of $\"\"$ .

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$\"\"$

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Compare $\"\"$ - coefficients and constant terms.

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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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Substitute $\"\"$ and $\"\"$ in $\"\"$

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$\"\"$

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

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$\"\"$

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$\"\"$ .

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Solution:

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$\"\"$ .