2.1.20.7 ✓ Mathematica. Time used: 0.035 (sec). Leaf size: 15

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

\begin{align*} x(t)&\to c_1 \cos (t)\\ x(t)&\to 0 \end{align*}