$\"\"$ \ \

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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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Let $\"\"$ . \ \

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Apply derivative on each side. \ \

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$\"\"$ \ \

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$\"\"$ . \ \

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

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

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$\"\"$ \ \

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