Solve the given differential equation by separation of varia

Solve the given differential equation by separation of variables. Dy/dx=xy+3x-y-3/xy-4x+6y-24 (x+6/y+3)^7=

dy/dx = (x - 1)(y + 3) / (x + 6)(y - 4)

(y - 4)*dy / (y + 3) = (x - 1)*dx / (x + 6)

(y-4)/(y+3) is to be written as : 1 - 7/(y+3)
(x - 1)/(x + 6) written as 1 - 7/(x + 6)

( 1 - 7/(y+3)) * dy = (1 - 7/(x + 6)) * dx

Integrating :

y - 7ln|y + 3| = x - 7ln|x + 6| + C

7ln|x + 6| - 7ln|y + 3| = x - y + C

ln|(x + 6)^7 / (y + 3)^7| = x - y + C

((x + 6)/(y + 3))^7 = e^(x - y + C)

((x + 6)/(y + 3))^7 = Ce^(x - y) ---> ANSWER