What is the solution for (dy)/(dx)=(xy)/(x^2-3x+2) ?

The solution for (dy)/(dx)=(xy)/(x^2-3x+2) is y=e^{2(1/4 ln(4x^2-12x+8)-3/4 ln((x-1)/(x-2)))+c_{1}}

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(dy)/(dx)=(xy)/(x^2-3x+2)

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

y = e^{2 (\frac{1}{4} l n (4 x^{2} - 12 x + 8) - \frac{3}{4} l n (\frac{x - 1}{x - 2})) + c_{1}}

Solution steps

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

Solve separable ODE:

y = e^{2 (\frac{1}{4} l n (4 x^{2} - 12 x + 8) - \frac{3}{4} l n (\frac{x - 1}{x - 2})) + c_{1}}

y = e^{2 (\frac{1}{4} l n (4 x^{2} - 12 x + 8) - \frac{3}{4} l n (\frac{x - 1}{x - 2})) + c_{1}}

\frac{d v}{d t} = 8 - 3 v

(y^{2} + 2 y - 3) d x + (4 x y + 4 x) d y = 0

\frac{d y}{d x} = - \frac{3}{5} x^{5} y^{7}

y^{^{'}} = 6 x y - 5 x, y (0) = 1

\frac{d y}{d x} = - \frac{3}{5} x^{6} y^{4}

What is the solution for (dy)/(dx)=(xy)/(x^2-3x+2) ?
The solution for (dy)/(dx)=(xy)/(x^2-3x+2) is y=e^{2(1/4 ln(4x^2-12x+8)-3/4 ln((x-1)/(x-2)))+c_{1}}