$\"\"$

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The bernoulli differential equation is $\"\"$ .

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$\"\"$

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Multiply on each side by $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ .

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Apply derivative on each side. \ \

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$\"\"$ .

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Substitute $\"\"$ and $\"\"$ in the modified function.

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$\"\"$

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$\"\"$

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$\"\"$ .

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The equation is in the form of linear equation $\"\"$ .

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Here $\"\"$ and $\"\"$ .

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The integrating factor is $\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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The general solution is $\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The solution of bernoulli differential equation is $\"\"$ .

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$\"\"$

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The solution of bernoulli differential equation is $\"\"$ .