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

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}