Answer to Question #168097 in Differential Equations for sergio

Question

dy/dx = y(20 - 4y)

Answer 1

$$\frac{dy}{dx}=y(20-4y)$$ $$\frac{dy}{y(5-y)}=4dx$$ $$\int\frac{dy}{y(5-y)}=\int4dx$$ $$\int\frac{1}{5}(\frac{1}{y}+\frac{1}{5-y})dy=\int4dx$$ $$\frac{1}{5}\ln |y|-\frac{1}{5}\ln|y-5|=4x+C,$$

where $C$ is some constant.

$$\ln{\frac{y}{y-5}}=20x+C_1,$$

or

$$y=\frac{5}{C_2e^{-20x}+1}.$$

Answer. $y=\frac{5}{C_2e^{-20x}+1}.$