Question

dy/dx= 3 cos 2x -(2/x^2)

Answer 1

y = 3/2 sin2x +2/x

Answer 2

Yay, I got first!

Answer 3

Integrate both sides with respect to x:
y(x) = integral (-2/x^2+3 cos(2 x)) dx = 2/x+3/2 sin(2 x)+c_1, where c_1 is an arbitrary constant.