2.3.1.5 ✓ Mathematica. Time used: 0.016 (sec). Leaf size: 27

ode=D[x[t],{t,2}]-x[t]==t^2; 
ic={x[0]==0,Derivative[1][x][0] == 1}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {1}{2} \left (-2 \left (t^2+2\right )+e^{-t}+3 e^t\right ) \end{align*}