\[ y(x) \left (a e^{2 x}+b e^x+c\right )+y''(x)=0 \] ✓ Mathematica : cpu = 0.496692 (sec), leaf count = 180
DSolve[(c + b*E^x + a*E^(2*x))*y[x] + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 e^{i \left (\sqrt {c} \log \left (e^x\right )-\sqrt {a} e^x\right )} U\left (\frac {i \left (b-i \sqrt {a}+2 \sqrt {a} \sqrt {c}\right )}{2 \sqrt {a}},2 i \sqrt {c}+1,2 i \sqrt {a} e^x\right )+c_2 e^{i \left (\sqrt {c} \log \left (e^x\right )-\sqrt {a} e^x\right )} L_{-\frac {i \left (b-i \sqrt {a}+2 \sqrt {a} \sqrt {c}\right )}{2 \sqrt {a}}}^{2 i \sqrt {c}}\left (2 i \sqrt {a} e^x\right )\right \}\right \}\] ✓ Maple : cpu = 0.196 (sec), leaf count = 58
dsolve(diff(diff(y(x),x),x)+(a*exp(2*x)+b*exp(x)+c)*y(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{-\frac {x}{2}} \left (\WhittakerM \left (-\frac {i b}{2 \sqrt {a}}, i \sqrt {c}, 2 i \sqrt {a}\, {\mathrm e}^{x}\right ) c_{1}+\WhittakerW \left (-\frac {i b}{2 \sqrt {a}}, i \sqrt {c}, 2 i \sqrt {a}\, {\mathrm e}^{x}\right ) c_{2}\right )\]