\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) - \left ( 2\,{{\rm e}^{x}}+1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +{{\rm e}^{2\,x}}y \left ( x \right ) -{{\rm e}^{3\,x}}=0} \]
Mathematica: cpu = 0.040505 (sec), leaf count = 28 \[ \left \{\left \{y(x)\to c_1 e^{e^x}+c_2 e^{x+e^x}+e^x+2\right \}\right \} \]
Maple: cpu = 0.125 (sec), leaf count = 66 \[ \left \{ y \left ( x \right ) ={{\rm e}^{{{\rm e}^{x}}+{\frac {x}{2}}}} \sinh \left ( {\frac {x}{2}} \right ) {\it \_C2}+{{\rm e}^{{{\rm e}^{x}} +{\frac {x}{2}}}}\cosh \left ( {\frac {x}{2}} \right ) {\it \_C1}+{ {\rm e}^{{\frac {x}{2}}}} \left ( \left ( {{\rm e}^{2\,x}}+{{\rm e}^{x} }+1 \right ) \cosh \left ( {\frac {x}{2}} \right ) -3\, \left ( {{\rm e}^{ x}}+1/3\,{{\rm e}^{2\,x}}+1 \right ) \sinh \left ( x/2 \right ) \right ) \right \} \]