Nd solve delay differential equations read

sol = NDSolve[{x''[t] + x[t - 1] == 0, x[t /; t ≤ 0] == t ^ 2}, x, {t, -1, 5}]

NDSolve[{x[-1 + t] + Derivative[2][x][t] == 0, x[t /; t <= 0] == t^2}, x, {t, -1, 5}]

Plot[Evaluate[{x[t], x'[t], x''[t]} /. First[sol]], {t, -1, 5}, PlotRange -> All]

-Graphics-

nsol = NDSolve[{x''[t] + x[t + 1] == 0, x[t /; t ≥   0] == t ^ 2}, x, {t, -5, 1}];
Plot[Evaluate[{x[t], x'[t], x''[t]} /. First[nsol]], {t, -5, 1}, PlotRange -> All]

-Graphics-