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}}

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)}