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

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

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(dy)/(dx)=(y-1)^2

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{1}{( 1 - x )}

\int sin (x) cos^{4} (d) x d x

y^{^{'}} = \frac{( e ^{x - y} )}{( 1 + e ^{x} )}

\frac{d}{d x} (csc^{2} (x) - 3)

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