$\"\"$

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

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Consider $\"\"$ .

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Multiply each side by $\"\"$ .

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$\"\"$

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$\"\"$

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Let $\"\"$ and $\"\"$

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

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$\"\"$

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It is in the general form of linear equation $\"\"$ .

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In the above equation , $\"\"$ and $\"\"$ .

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The integrating factor is $\"\"$ .

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Substitute $\"\"$ in the above formula.

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$\"\"$

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$\"\"$

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The general solution is $\"\"$ .

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Resubstitute $\"\"$ , substitute $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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Therefore, the general solution is $\"\"$ .

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$\"\"$

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