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

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

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

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

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

Solution steps

d y - (y - 1)^{2} d x = 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 \to 1 lim (2 x^{3} - 5 x^{2} + x + 6)

\int cot^{3} (x) csc^{3} (x) d x

\frac{d}{d x} ((x^{3} - 4 x^{2} - 6 x + 1) (x^{2} - 3 x + 1))

\frac{d}{d x} (x (2 x + 3)^{5})

13 e^{4 t} e^{2}

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