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{d y}{d t} = 6 y^{2}

f (x) = ln (x)

f (x) = 4 x + 1

x \to 0 - lim (x^{2} (sin (\frac{1}{x})))

\frac{d}{d x} (\frac{2 x + 1}{x + 5})

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)}