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Question Number 101841 by bemath last updated on 05/Jul/20

$${xy}^{\prime }+y=y^2$$

Answered by bobhans last updated on 05/Jul/20

$${xy}^{\prime }=y^2-y\Rightarrow \frac{dy}{y(y-1)}=\frac{dx}{x}$$$$\int \frac{dy}{y-1}-\int \frac{dy}{y}=\frac{dx}{x}$$$$\ln \left(\frac{y-1}{y}\right)=\ln \mid Cx\mid \Rightarrow 1-\frac{1}{y}=\mid Cx\mid$$$$\frac{1}{y}=1-\mid Cx\mid \iff y=\frac{1}{1-\mid Cx\mid }(Bob-)$$

Commented by bemath last updated on 05/Jul/20

macho......^o^

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