Verified answer

Hola

x y + 3 x - y - 3 = x (y + 3) - ( y + 3) = (x - 1) (y + 3)

x y - 2 x + 4 y - 8 = x (y - 2) + 4 ( y - 2) = (x + 4) (y - 2)

Queda

dy/dx = ( (x - 1) (y + 3) ) / ( (x + 4) (y - 2) )

Separamos variables

(y - 2) dy/(y + 3) = (x - 1) dx / (x + 4)

(y + 3 - 5) dy/(y + 3) = (x + 4 - 5 ) dx / (x + 4)

(y + 3) dy/(y + 3) - 5 (dy/(y + 3)) =

= (x + 4) dx / (x + 4) - 5 (dx / (x + 4))

dy - 5 (dy/(y + 3)) = dx - 5 (dx / (x + 4))

Ya podemos integrar

y - 5 ln(y + 3) = x - 5 ln(x + 4) + C

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