\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +ay \left ( x \right ) -c{{\rm e}^{bx}}=0} \]
Mathematica: cpu = 0.014502 (sec), leaf count = 34 \[ \left \{\left \{y(x)\to \frac {c e^{x (a+b)-a x}}{a+b}+c_1 e^{-a x}\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 25 \[ \left \{ y \left ( x \right ) = \left ( {\frac {c{{\rm e}^{ \left ( a+b \right ) x}}}{a+b}}+{\it \_C1} \right ) {{\rm e}^{-ax}} \right \} \]
Sage: cpu = 0.008 (sec), leaf count = 0 \[ \left [{\left (c + \frac {c e^{\left (a x + b x\right )}}{a + b}\right )} e^{\left (-a x\right )}, \text {\texttt {linear}}\right ] \]