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 \frac{1}{4 x + 5 x} d x

\frac{\partial}{\partial y} (2 cos (x))

\frac{d}{d x} (7 e^{- x} + e^{4 x})

\int \frac{9 + x ^{2}}{x} d x

d er i v a t i v e \frac{1}{2} x

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}