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

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

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

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

y = - \frac{1}{x + c _{1}} + \frac{2 x}{x + c _{1}} + \frac{2 c _{1}}{x + c _{1}}

Solution steps

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

Solve separable ODE:

y = - \frac{1}{x + c _{1}} + \frac{2 x}{x + c _{1}} + \frac{2 c _{1}}{x + c _{1}}

y = - \frac{1}{x + c _{1}} + \frac{2 x}{x + c _{1}} + \frac{2 c _{1}}{x + c _{1}}

\int_{- 2 π}^{π} cos^{2} (x) d x

x \to \infty lim ((1 + (\frac{2}{x}))^{3 x})

x \to 4 lim (\frac{- 1}{x ^{2} - 16})

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

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