What is the solution for (dy)/(dx)=(x-1)/(y-3) ?

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

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(dy)/(dx)=(x-1)/(y-3)

\frac{d y}{d x} = \frac{x - 1}{y - 3}

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

Solution steps

\frac{d y}{d x} = \frac{x - 1}{y - 3}

Solve separable ODE:

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

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

y = \frac{5}{3}, y = \frac{1}{4 - x ^{2}}

\frac{d}{d t} (2 + t)

\int 2 x^{3} + 3 x d x

(\frac{x + 5}{x - 5})^{5}

x \to 0 + lim (\frac{1}{x ^{2} - x})

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