Given N(x,y) y' + M(x,y) = 0, then IF -- can write it as N(y) y' + M(x) = 0 -- where N is function of y only and M function of x only THEN -- separable, i.e. @N/@x = @M/@y = 0 -- example: y' + x = 0 or y*y' + x+sin(x)=0 (linear) -- solve as separable, but some non-linear separable have no solution -- example: (1/ln(y)) y' + x = 0 ELSE IF @N/@x = @M/@y THEN -- exact -- example (2 x y +1) y' + (x +y^2) = 0 -- solve using phi(x,y) potential function method ELSE -- not exact IF bernulli -- check for special case -- ELSE -- use generalized integrating factor END IF END IF END IF