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

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

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

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

y = \frac{x ^{2}}{2 ( x - 3 )} - \frac{3 x}{x - 3} + \frac{c _{1}}{x - 3}

Solution steps

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

Solve linear ODE:

y = \frac{x ^{2}}{2 ( x - 3 )} - \frac{3 x}{x - 3} + \frac{c _{1}}{x - 3}

y = \frac{x ^{2}}{2 ( x - 3 )} - \frac{3 x}{x - 3} + \frac{c _{1}}{x - 3}

\frac{1}{0.012 s ^{2} + 1.55 s + 50}

s \to 1 lim (\frac{( 2 s + 3 )}{s})

\frac{d y}{d x} = 2 y + 3

\int_{1}^{8} (x^{2} - 4 x + 6) d x

f (x) = ln (x - x^{2})

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