Find the equation that doesn't have a series solution in form of $$y(x)=\sum_{n=0}^{\infty}a_nx^n $$
$$ 1.\;\;\frac{d^2y}{dx^2}+\frac{\sin x}{x}y=0 \qquad 2.\;\;\frac{d^2y}{dx^2}+\frac{\cos x}{x}y=0$$ $$ 3.\;\;\frac{d^2y}{dx^2}+{\sin(x)}y=0\qquad 4.\;\;\frac{d^2y}{dx^2}+{\cos(x)}y=0$$
$y''+P(x)y'+Q(x)y=0 $
It seems $Q(x)$ in every choice is analytic to me. How should I solve it?