What is the solution for (dy)/(dt)=4y(1-y) ?

The solution for (dy)/(dt)=4y(1-y) is y=-(e^{4t+c_{1}})/(1-e^{4t+c_{1)}}

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(dy)/(dt)=4y(1-y)

\frac{d y}{d t} = 4 y (1 - y)

y = - \frac{e ^{4 t + c_{1}}}{1 - e ^{4 t + c_{1}}}

Solution steps

\frac{d y}{d t} = 4 y (1 - y)

Solve separable ODE:

y = - \frac{e ^{4 t + c_{1}}}{1 - e ^{4 t + c_{1}}}

y = - \frac{e ^{4 t + c_{1}}}{1 - e ^{4 t + c_{1}}}

\int_{1}^{2} \frac{2}{x ^{3} + x} d x

e^{3 t}

x \to 2 lim (x 4 - x^{2})

\int x^{2} + \frac{1}{( 3 x ) ^{2}} d x

What is the solution for (dy)/(dt)=4y(1-y) ?
The solution for (dy)/(dt)=4y(1-y) is y=-(e^{4t+c_{1}})/(1-e^{4t+c_{1)}}