What is the solution for dy-(y-8)^2dx=0 ?

The solution for dy-(y-8)^2dx=0 is y=-1/(x+c_{1)}+(8x)/(x+c_{1)}+(8c_{1})/(x+c_{1)}

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dy-(y-8)^2dx=0

d y - (y - 8)^{2} d x = 0

y = - \frac{1}{x + c _{1}} + \frac{8 x}{x + c _{1}} + \frac{8 c _{1}}{x + c _{1}}

Solution steps

d y - (y - 8)^{2} d x = 0

Solve separable ODE:

y = - \frac{1}{x + c _{1}} + \frac{8 x}{x + c _{1}} + \frac{8 c _{1}}{x + c _{1}}

y = - \frac{1}{x + c _{1}} + \frac{8 x}{x + c _{1}} + \frac{8 c _{1}}{x + c _{1}}

\frac{\partial}{\partial x} (x^{2} y^{3} + (x - y)^{2})

x y^{^{'}} + y = - 3 x y^{2}, y (1) = 4

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What is the solution for dy-(y-8)^2dx=0 ?
The solution for dy-(y-8)^2dx=0 is y=-1/(x+c_{1)}+(8x)/(x+c_{1)}+(8c_{1})/(x+c_{1)}