2.1.19.5 ✓ Mathematica. Time used: 0.04 (sec). Leaf size: 21

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

\begin{align*} x(t)&\to \frac {e^t}{3}+c_1 e^{-2 t} \end{align*}