What is the solution for (dy)/(dt)=e^t(y-1)^2 ?

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

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(dy)/(dt)=e^t(y-1)^2

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

y = - \frac{1}{e ^{t} + c _{1}} + \frac{e ^{t}}{e ^{t} + c _{1}} + \frac{c _{1}}{e ^{t} + c _{1}}

Solution steps

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

Solve separable ODE:

y = - \frac{1}{e ^{t} + c _{1}} + \frac{e ^{t}}{e ^{t} + c _{1}} + \frac{c _{1}}{e ^{t} + c _{1}}

y = - \frac{1}{e ^{t} + c _{1}} + \frac{e ^{t}}{e ^{t} + c _{1}} + \frac{c _{1}}{e ^{t} + c _{1}}

ln (3 x) - \frac{1}{6} x

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

\int \frac{1}{x} sin (x) d x

\int \frac{x}{( x ^{2} + 1 ) ( x ^{2} + 4 )} d x

\int (1 + 0.5 t) e^{- 0.004 t} d t

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