2.1.2.5 ✓ Mathematica. Time used: 0.042 (sec). Leaf size: 29

ode=D[y[x],x]+c*y[x]==a; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {a}{c}+c_1 e^{-c x}\\ y(x)&\to \frac {a}{c} \end{align*}