What is the solution for (dy)/(dt)=10y-2y^2 ?

The solution for (dy)/(dt)=10y-2y^2 is y=-(5e^{10t+5c_{1}})/(1-e^{5(2t+c_{1))}}

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(dy)/(dt)=10y-2y^2

\frac{d y}{d t} = 10 y - 2 y^{2}

y = - \frac{5 e ^{10 t + 5 c_{1}}}{1 - e ^{5 (2 t + c_{1})}}

Solution steps

\frac{d y}{d t} = 10 y - 2 y^{2}

Solve separable ODE:

y = - \frac{5 e ^{10 t + 5 c_{1}}}{1 - e ^{5 (2 t + c_{1})}}

y = - \frac{5 e ^{10 t + 5 c_{1}}}{1 - e ^{5 (2 t + c_{1})}}

y^{- 1} d y + y \cdot e^{c o s (x)} \cdot sin (x) d x = 0

\frac{d y}{d x} = (\frac{2 x + x y ^{2}}{4 y + y x ^{2}})

\frac{d y}{d x} = x y^{2}, y (1) = 1

y^{^{'}} - 5 x^{3} e^{y} = 0

\frac{d y}{d x} = 1 y + y^{2}

What is the solution for (dy)/(dt)=10y-2y^2 ?
The solution for (dy)/(dt)=10y-2y^2 is y=-(5e^{10t+5c_{1}})/(1-e^{5(2t+c_{1))}}