# What is a solution to the differential equation dy/dt=e^t(y−1)^2?

What is a solution to the differential equation $\frac{dy}{dt}={e}^{t}{\left(y-1\right)}^{2}$?
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blikath3
We have:
$\frac{dy}{dt}={e}^{t}{\left(y-1\right)}^{2}$
We can collect terms for similar variables:

Which is a separable First Order Ordinary non-linear Differential Equation, so we can "separate the variables" to get:

Both integrals are those of standard functions, so we can use that knowledge to directly integrate:
$-\frac{1}{y-1}={e}^{t}+C$
And we can readily rearrange for y:
$-\left(y-1\right)=\frac{1}{{e}^{t}+C}$
$\therefore 1-y=\frac{1}{{e}^{t}+C}$
$y=1-\frac{1}{{e}^{t}+C}$