To describe the motion of a pendulum subject to small random perturbations, consider the equation y''(t) + (1 + ε dWt/dt)y = 0. How would you solve this equation in terms of y(0) and y'(0)?
a) y(t) = y(0) cos(t) + y'(0) sin(t)
b) y(t) = y(0) sin(t) + y'(0) cos(t)
c) y(t) = y(0) et + y'(0) e(-t)
d) y(t) = y(0) cos(t) - y'(0) sin(t)