\[ (a x+b) y'(x)+y(x) \left (\text {a1} x^2+\text {b1} x+\text {c1}\right )+y''(x)=0 \] ✓ Mathematica : cpu = 0.138796 (sec), leaf count = 421
\[\left \{\left \{y(x)\to c_1 \exp \left (\frac {-b x \sqrt {a^2-4 \text {a1}}-\frac {1}{2} a x^2 \sqrt {a^2-4 \text {a1}}-\frac {1}{2} a^2 x^2-a b x+2 \text {a1} x^2+2 \text {b1} x}{2 \sqrt {a^2-4 \text {a1}}}\right ) H_{\frac {-a^3+2 \text {c1} a^2-\sqrt {a^2-4 \text {a1}} a^2+4 \text {a1} a-2 b \text {b1} a+2 \text {a1} b^2+2 \text {b1}^2+4 \sqrt {a^2-4 \text {a1}} \text {a1}-8 \text {a1} \text {c1}}{2 \left (a^2-4 \text {a1}\right )^{3/2}}}\left (\frac {a b-2 \text {b1}}{\sqrt {2} \left (a^2-4 \text {a1}\right )^{3/4}}+\frac {\sqrt [4]{a^2-4 \text {a1}} x}{\sqrt {2}}\right )+c_2 \exp \left (\frac {-b x \sqrt {a^2-4 \text {a1}}-\frac {1}{2} a x^2 \sqrt {a^2-4 \text {a1}}-\frac {1}{2} a^2 x^2-a b x+2 \text {a1} x^2+2 \text {b1} x}{2 \sqrt {a^2-4 \text {a1}}}\right ) \, _1F_1\left (-\frac {-a^3+2 \text {c1} a^2-\sqrt {a^2-4 \text {a1}} a^2+4 \text {a1} a-2 b \text {b1} a+2 \text {a1} b^2+2 \text {b1}^2+4 \sqrt {a^2-4 \text {a1}} \text {a1}-8 \text {a1} \text {c1}}{4 \left (a^2-4 \text {a1}\right )^{3/2}};\frac {1}{2};\left (\frac {a b-2 \text {b1}}{\sqrt {2} \left (a^2-4 \text {a1}\right )^{3/4}}+\frac {\sqrt [4]{a^2-4 \text {a1}} x}{\sqrt {2}}\right )^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.451 (sec), leaf count = 262
\[ \left \{ y \left ( x \right ) = \left ( {\it \_C2}\, \left ( {a}^{2}x+ab-4\,{\it a1}\,x-2\,{\it b1} \right ) {\mbox {$_1$F$_1$}({\frac {1}{4} \left ( 3\, \left ( {a}^{2}-4\,{\it a1} \right ) ^{3/2}+{a}^{3}-2\,{a}^{2}{\it c1}+ \left ( 2\,{\it b1}\,b-4\,{\it a1} \right ) a+ \left ( -2\,{b}^{2}+8\,{\it c1} \right ) {\it a1}-2\,{{\it b1}}^{2} \right ) \left ( {a}^{2}-4\,{\it a1} \right ) ^{-{\frac {3}{2}}}};\,{\frac {3}{2}};\,{\frac { \left ( {a}^{2}x+ab-4\,{\it a1}\,x-2\,{\it b1} \right ) ^{2}}{2} \left ( {a}^{2}-4\,{\it a1} \right ) ^{-{\frac {3}{2}}}})}+{\it \_C1}\,{\mbox {$_1$F$_1$}({\frac {1}{4} \left ( \left ( {a}^{2}-4\,{\it a1} \right ) ^{{\frac {3}{2}}}+{a}^{3}-2\,{a}^{2}{\it c1}+ \left ( 2\,{\it b1}\,b-4\,{\it a1} \right ) a+ \left ( -2\,{b}^{2}+8\,{\it c1} \right ) {\it a1}-2\,{{\it b1}}^{2} \right ) \left ( {a}^{2}-4\,{\it a1} \right ) ^{-{\frac {3}{2}}}};\,{\frac {1}{2}};\,{\frac { \left ( {a}^{2}x+ab-4\,{\it a1}\,x-2\,{\it b1} \right ) ^{2}}{2} \left ( {a}^{2}-4\,{\it a1} \right ) ^{-{\frac {3}{2}}}})} \right ) {{\rm e}^{-{\frac {x}{4} \left ( \left ( ax+2\,b \right ) \left ( {a}^{2}-4\,{\it a1} \right ) ^{{\frac {3}{2}}}+ \left ( {a}^{2}-4\,{\it a1} \right ) \left ( {a}^{2}x+2\,ab-4\,{\it a1}\,x-4\,{\it b1} \right ) \right ) \left ( {a}^{2}-4\,{\it a1} \right ) ^{-{\frac {3}{2}}}}}} \right \} \]