What is the solution for dy-(y-6)^2dx=0 ?

The solution for dy-(y-6)^2dx=0 is y=-1/(x+c_{1)}+(6x)/(x+c_{1)}+(6c_{1})/(x+c_{1)}

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dy-(y-6)^2dx=0

d y - (y - 6)^{2} d x = 0

y = - \frac{1}{x + c _{1}} + \frac{6 x}{x + c _{1}} + \frac{6 c _{1}}{x + c _{1}}

Solution steps

d y - (y - 6)^{2} d x = 0

Solve separable ODE:

y = - \frac{1}{x + c _{1}} + \frac{6 x}{x + c _{1}} + \frac{6 c _{1}}{x + c _{1}}

y = - \frac{1}{x + c _{1}} + \frac{6 x}{x + c _{1}} + \frac{6 c _{1}}{x + c _{1}}

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

x \to - 1 lim (\frac{3 - 4 x}{x})

5^{2 y}

\frac{d y}{d x} = x^{4} (y - 2)

What is the solution for dy-(y-6)^2dx=0 ?
The solution for dy-(y-6)^2dx=0 is y=-1/(x+c_{1)}+(6x)/(x+c_{1)}+(6c_{1})/(x+c_{1)}