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Question Number 184066 by Matica last updated on 02/Jan/23

$$\frac{dy}{dx}=y(y+2).findy=?$$

Answered by mr W last updated on 02/Jan/23

$$\int \frac{dy}{y(y+2)}=\int dx$$$$\int (\frac{1}{y}-\frac{1}{y+2})dy=2\int dx$$$$\ln y-\ln (y+2)=2x+C_1$$$$\ln \frac{y}{y+2}=2x+C_1$$$$\frac{y}{y+2}={Ce}^{2x}$$$$\Rightarrow y=\frac{2}{1-{Ce}^{2x}}-2$$

Commented by Matica last updated on 02/Jan/23

$$Ok.Thankyou.$$

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