If an equation of the form
dy/dx = [a1x+b1y+c1]/[a2x+b2y+c2] is given
Put x = X+h and y = Y+k
where h and k constants.
h and k are to be determined.
Their values are
h/(b1c2-b2c1) = k/(c1a2-c2a1) = 1/(a1b2-a2b1)
This substitution will give the transformed equations
dY/dX = (a1X + b1Y)/(a2X + b2Y)
The above equation is a homogeneous differential equation.
Solve it and substitute X = x-h and Y = y-k