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

\int_{2}^{\infty} \frac{3}{x ^{2} - x} d x

y = x^{3} - x, y = 7 x - x^{3}

\frac{\partial}{\partial y} (6 ln (6 x^{3} + y^{2}))

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

\frac{d y}{d x}, e^{\frac{x}{y}} = 4 x - y

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}