What is the solution for dy-dx(y-1)^2=0 ?

The solution for dy-dx(y-1)^2=0 is y=-1/(x+c_{1)}+x/(x+c_{1)}+(c_{1})/(x+c_{1)}

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dy-dx(y-1)^2=0

d y - d x (y - 1)^{2} = 0

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

Solution steps

d y - d x (y - 1)^{2} = 0

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}}

(x + x) \frac{d y}{d x} = (y + y)

x y^{^{'}} + y = 0

\frac{d x}{d t} = 7 x t^{3}

y^{^{'}} = x \cdot e^{y}

(x^{3} + 7 x^{3} y^{2}) d x + e^{x^{4}} y d y = 0

What is the solution for dy-dx(y-1)^2=0 ?
The solution for dy-dx(y-1)^2=0 is y=-1/(x+c_{1)}+x/(x+c_{1)}+(c_{1})/(x+c_{1)}