ordinary differential equations – Solutions to the ODE $exp(D)x=0$

Let $D$ denote the differential operator and let $exp(D)$ denote the exponential function of the differential operator, that is, $exp(D)=I+D+D^2/2+…$. What are the solutions to the ODE $exp(D)x=0$? Put differently, what are the solutions to the ODE $x+x’+x”/2+…=0$