Solve. dy/dx = xy(1-y)

Glenn Hopkins
2022-07-31
Answered

Solve. dy/dx = xy(1-y)

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ab8s1k28q

Answered 2022-08-01
Author has **17** answers

dy/dx = xy(1-y)

dy/[y(1-y)] = xdx

$\int \frac{1}{y(1-y)}dy=\int [\frac{1}{y}+\frac{1}{1-y}]dy=\int xdx$

$\mathrm{ln}y-\mathrm{ln}(1-y)=\frac{1}{2}{x}^{2}+C$

$\mathrm{ln}(\frac{y}{1-y})=\frac{1}{2}{x}^{2}+C$

$\frac{y}{1-y}={e}^{\frac{{x}^{2}}{2}+C}=D{e}^{\frac{{x}^{2}}{2}}$

dy/[y(1-y)] = xdx

$\int \frac{1}{y(1-y)}dy=\int [\frac{1}{y}+\frac{1}{1-y}]dy=\int xdx$

$\mathrm{ln}y-\mathrm{ln}(1-y)=\frac{1}{2}{x}^{2}+C$

$\mathrm{ln}(\frac{y}{1-y})=\frac{1}{2}{x}^{2}+C$

$\frac{y}{1-y}={e}^{\frac{{x}^{2}}{2}+C}=D{e}^{\frac{{x}^{2}}{2}}$

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