Using: d tan^-1 (x/y)=(y dx - x dy)/(x^2 + y^2), and ½ d ln(x^2 + y^2)=(x dx + y dy)/(x^2 + y^2) find integrating factors for, and solve, the following equation:
(2x^(2)y + 2y^3 - x) (dy/dx) + y=0
your tan^-1 (x/y) means tan(x/y). Then the formula
d tan^-1 (x/y)=(y dx - x ...
This shows how to find integrating factors and solve an equation.