$\"\"$

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

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Consider the function $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$ .

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Susbtitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Susbtitute $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ .

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$\"\"$ .

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$ .

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Therefore, if $\"\"$ , $\"\"$ the bernoulli equation is a linear equation.

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$\"\"$

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

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