The slowly varying oscillator equation is y'' + q(εx)2y = 0, where ε ≪ 1 and q is strictly positive. Find an approximate solution. Why is the equation called slowly varying?

a) The approximate solution is y(x) ≈ cos(εx) + O(ε3), it is called slowly varying because the amplitude changes slowly with x.
b) The approximate solution is y(x) ≈ sin(εx) + O(ε2), it is called slowly varying because the frequency changes slowly with x.
c) The approximate solution is y(x) ≈ e(εx) + O(ε2), it is called slowly varying because the exponential growth is slow.
d) The approximate solution is y(x) ≈ 1 + O(ε), it is called slowly varying because the solution remains close to 1.