2.2.11.5 ✓ Mathematica. Time used: 0.016 (sec). Leaf size: 11

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

\begin{align*} x(t)&\to e^t \sin (t) \end{align*}