What is the solution for (dy)/(dx)=(y-5)^2 ?

The solution for (dy)/(dx)=(y-5)^2 is y=-1/(x+c_{1)}+(5x)/(x+c_{1)}+(5c_{1})/(x+c_{1)}

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(dy)/(dx)=(y-5)^2

\frac{d y}{d x} = (y - 5)^{2}

y = - \frac{1}{x + c _{1}} + \frac{5 x}{x + c _{1}} + \frac{5 c _{1}}{x + c _{1}}

Solution steps

\frac{d y}{d x} = (y - 5)^{2}

Solve separable ODE:

y = - \frac{1}{x + c _{1}} + \frac{5 x}{x + c _{1}} + \frac{5 c _{1}}{x + c _{1}}

y = - \frac{1}{x + c _{1}} + \frac{5 x}{x + c _{1}} + \frac{5 c _{1}}{x + c _{1}}

\frac{d y}{d x}

\frac{- 14 x}{12 y}

y = \frac{1}{2} x^{2}, y = - x^{2} + 6

\int x \cdot ln (x - 1) d x

2 x \frac{d y}{d x} - y = 3 x^{2}

What is the solution for (dy)/(dx)=(y-5)^2 ?
The solution for (dy)/(dx)=(y-5)^2 is y=-1/(x+c_{1)}+(5x)/(x+c_{1)}+(5c_{1})/(x+c_{1)}