What is the solution for (dx)/(dt)=-1+(x+t-1)^2 ?

The solution for (dx)/(dt)=-1+(x+t-1)^2 is x=-1/(t+c_{1)}-t+1

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(dx)/(dt)=-1+(x+t-1)^2

\frac{d x}{d t} = - 1 + (x + t - 1)^{2}

x = - \frac{1}{t + c _{1}} - t + 1

Solution steps

\frac{d x}{d t} = - 1 + (x + t - 1)^{2}

Solve using substitution:

x = - \frac{1}{t + c _{1}} - t + 1

x = - \frac{1}{t + c _{1}} - t + 1

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