2.1.14.5 ✓ Mathematica. Time used: 0.003 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to \frac {a x^2}{2 c}+c_1 \end{align*}