\[ (a x+b) y'(x)+y(x) \left (\text {a1} x^2+\text {b1} x+\text {c1}\right )+y''(x)=0 \] ✓ Mathematica : cpu = 0.22678 (sec), leaf count = 305
\[\left \{\left \{y(x)\to \exp \left (-\frac {x \left (a \left (x \sqrt {a^2-4 \text {a1}}+2 b\right )+2 b \sqrt {a^2-4 \text {a1}}+a^2 x-4 (\text {a1} x+\text {b1})\right )}{4 \sqrt {a^2-4 \text {a1}}}\right ) \left (c_1 H_{\frac {-a^3-\left (\sqrt {a^2-4 \text {a1}}-2 \text {c1}\right ) a^2+(4 \text {a1}-2 b \text {b1}) a+2 \left (\text {b1}^2+\text {a1} \left (b^2-4 \text {c1}+2 \sqrt {a^2-4 \text {a1}}\right )\right )}{2 \left (a^2-4 \text {a1}\right )^{3/2}}}\left (\frac {x a^2+b a-2 (\text {b1}+2 \text {a1} x)}{\sqrt {2} \left (a^2-4 \text {a1}\right )^{3/4}}\right )+c_2 \, _1F_1\left (\frac {a^3+\left (\sqrt {a^2-4 \text {a1}}-2 \text {c1}\right ) a^2+(2 b \text {b1}-4 \text {a1}) a-2 \left (\text {b1}^2+\text {a1} \left (b^2-4 \text {c1}+2 \sqrt {a^2-4 \text {a1}}\right )\right )}{4 \left (a^2-4 \text {a1}\right )^{3/2}};\frac {1}{2};\frac {\left (x a^2+b a-2 (\text {b1}+2 \text {a1} x)\right )^2}{2 \left (a^2-4 \text {a1}\right )^{3/2}}\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.307 (sec), leaf count = 262
\[ \left \{ y \left ( x \right ) = \left ( {\it \_C2}\, \left ( {a}^{2}x+ab-4\,{\it a1}\,x-2\,{\it b1} \right ) {\mbox {$_1$F$_1$}({\frac {1}{4} \left ( 3\, \left ( {a}^{2}-4\,{\it a1} \right ) ^{3/2}+{a}^{3}-2\,{a}^{2}{\it c1}+ \left ( 2\,{\it b1}\,b-4\,{\it a1} \right ) a+ \left ( -2\,{b}^{2}+8\,{\it c1} \right ) {\it a1}-2\,{{\it b1}}^{2} \right ) \left ( {a}^{2}-4\,{\it a1} \right ) ^{-{\frac {3}{2}}}};\,{\frac {3}{2}};\,{\frac { \left ( {a}^{2}x+ab-4\,{\it a1}\,x-2\,{\it b1} \right ) ^{2}}{2} \left ( {a}^{2}-4\,{\it a1} \right ) ^{-{\frac {3}{2}}}})}+{\it \_C1}\,{\mbox {$_1$F$_1$}({\frac {1}{4} \left ( \left ( {a}^{2}-4\,{\it a1} \right ) ^{{\frac {3}{2}}}+{a}^{3}-2\,{a}^{2}{\it c1}+ \left ( 2\,{\it b1}\,b-4\,{\it a1} \right ) a+ \left ( -2\,{b}^{2}+8\,{\it c1} \right ) {\it a1}-2\,{{\it b1}}^{2} \right ) \left ( {a}^{2}-4\,{\it a1} \right ) ^{-{\frac {3}{2}}}};\,{\frac {1}{2}};\,{\frac { \left ( {a}^{2}x+ab-4\,{\it a1}\,x-2\,{\it b1} \right ) ^{2}}{2} \left ( {a}^{2}-4\,{\it a1} \right ) ^{-{\frac {3}{2}}}})} \right ) {{\rm e}^{-{\frac {x}{4} \left ( \left ( ax+2\,b \right ) \left ( {a}^{2}-4\,{\it a1} \right ) ^{{\frac {3}{2}}}+ \left ( {a}^{2}-4\,{\it a1} \right ) \left ( {a}^{2}x+2\,ab-4\,{\it a1}\,x-4\,{\it b1} \right ) \right ) \left ( {a}^{2}-4\,{\it a1} \right ) ^{-{\frac {3}{2}}}}}} \right \} \]