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Differential equation y'=(Ay-a)(By-b)

With the constants A, a, B, b

$y^{'} (x) = (A y (x) - a) (B y (x) - b)$

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$y (x) = \frac{b e^{x (a B - A b)} - a C}{B e^{x (a B - A b)} - A C}$