2.1.5.5 ✓ Mathematica. Time used: 0.01 (sec). Leaf size: 12

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

\begin{align*} x(t)&\to \sin (t)-\sin (1) \end{align*}