What is the solution for (dy)/(dx)=((x-1))/(y-4) ?

The solution for (dy)/(dx)=((x-1))/(y-4) is y=4+sqrt(x^2-2x+c_{1)+16},y=4-sqrt(x^2-2x+c_{1)+16}

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(dy)/(dx)=((x-1))/(y-4)

\frac{d y}{d x} = \frac{( x - 1 )}{y - 4}

y = 4 + x^{2} - 2 x + c_{1} + 16, y = 4 - x^{2} - 2 x + c_{1} + 16

Solution steps

\frac{d y}{d x} = \frac{( x - 1 )}{y - 4}

Solve separable ODE:

y = 4 + x^{2} - 2 x + c_{1} + 16, y = 4 - x^{2} - 2 x + c_{1} + 16

y = 4 + x^{2} - 2 x + c_{1} + 16, y = 4 - x^{2} - 2 x + c_{1} + 16

y = \frac{1}{2} x + 8

f^{^{'}} (x) = x

\frac{d}{d x} (ln (- e^{- x} + e + 1))

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

y^{^{'}} = e^{y} 5^{x}

What is the solution for (dy)/(dx)=((x-1))/(y-4) ?
The solution for (dy)/(dx)=((x-1))/(y-4) is y=4+sqrt(x^2-2x+c_{1)+16},y=4-sqrt(x^2-2x+c_{1)+16}