What is the solution for (dy)/(dt)=y^2e^{-t},y(0)= 1/2 ,t>= 0 ?

The solution for (dy)/(dt)=y^2e^{-t},y(0)= 1/2 ,t>= 0 is y=(e^t)/(1+e^t)

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(dy)/(dt)=y^2e^{-t},y(0)= 1/2 ,t>= 0

\frac{d y}{d t} = y^{2} e^{- t}, y (0) = \frac{1}{2}, t \geq 0

y = \frac{e ^{t}}{1 + e ^{t}}

Solution steps

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

Solve separable ODE:

y = \frac{e ^{t}}{1 + e ^{t}}

y = \frac{e ^{t}}{1 + e ^{t}}

f (x) = \frac{1}{1 + x ^{2}} f^{^{'}} (x)

\frac{d y}{d x} = 7 x sec (y)

\frac{d y}{d x} y = tan (3 x^{4})

\frac{d y}{d x} = x^{5} (y - 2), y (0) = 6

y^{^{'}} + tan (2 \cdot x) y = 0, y (0) = 5

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