What is the solution for (dy)/(dx)=((x-3))/(y-3) ?

The solution for (dy)/(dx)=((x-3))/(y-3) is y=3+sqrt(x^2-6x+c_{1)+9},y=3-sqrt(x^2-6x+c_{1)+9}

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(dy)/(dx)=((x-3))/(y-3)

\frac{d y}{d x} = \frac{( x - 3 )}{y - 3}

y = 3 + x^{2} - 6 x + c_{1} + 9, y = 3 - x^{2} - 6 x + c_{1} + 9

Solution steps

\frac{d y}{d x} = \frac{( x - 3 )}{y - 3}

Solve separable ODE:

y = 3 + x^{2} - 6 x + c_{1} + 9, y = 3 - x^{2} - 6 x + c_{1} + 9

y = 3 + x^{2} - 6 x + c_{1} + 9, y = 3 - x^{2} - 6 x + c_{1} + 9

\int_{0}^{\infty} \frac{1}{1 + x} d x

\int 2 cos^{2} (θ) d θ

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

\frac{d ^{3}}{d x ^{3}} (x^{2} sin (x))

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

What is the solution for (dy)/(dx)=((x-3))/(y-3) ?
The solution for (dy)/(dx)=((x-3))/(y-3) is y=3+sqrt(x^2-6x+c_{1)+9},y=3-sqrt(x^2-6x+c_{1)+9}