What is the solution for (dy)/(dt)=4y+y^3,y(0)=1 ?

The solution for (dy)/(dt)=4y+y^3,y(0)=1 is y=(2e^{4t})/(sqrt(5-e^{8t))}

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(dy)/(dt)=4y+y^3,y(0)=1

\frac{d y}{d t} = 4 y + y^{3}, y (0) = 1

y = \frac{2 e ^{4 t}}{5 - e ^{8 t}}

Solution steps

\frac{d y}{d t} = 4 y + y^{3}

Solve Bernoulli ODE:

y = \frac{2 e ^{4 t}}{5 - e ^{8 t}}

y = \frac{2 e ^{4 t}}{5 - e ^{8 t}}

t e^{- 10 t}

\int \frac{1}{25 e ^{- 2 x} + e ^{2 x}} d x

y^{2} - 2 x = 9, x - y = 3

\int e^{x y^{2}} d x

What is the solution for (dy)/(dt)=4y+y^3,y(0)=1 ?
The solution for (dy)/(dt)=4y+y^3,y(0)=1 is y=(2e^{4t})/(sqrt(5-e^{8t))}