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(ax2+bx+c)d2dx2y(x)+(dx+f)ddxy(x)+gy(x)=0
Mathematica: cpu = 14.510843 (sec), leaf count = 56 \left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{g \unicode {f818}(\unicode {f817})+(\unicode {f817} d+f) \unicode {f818}'(\unicode {f817})+\left (a \unicode {f817}^2+b \unicode {f817}+c\right ) \unicode {f818}''(\unicode {f817})=0,\unicode {f818}(0)=c_1,\unicode {f818}'(0)=c_2\right \}\right )(x)\right \}\right \} \left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{g \unicode {f818}(\unicode {f817})+(\unicode {f817} d+f) \unicode {f818}'(\unicode {f817})+\left (a \unicode {f817}^2+b \unicode {f817}+c\right ) \unicode {f818}''(\unicode {f817})=0,\unicode {f818}(0)=c_1,\unicode {f818}'(0)=c_2\right \}\right )(x)\right \}\right \}
Maple: cpu = 0.140 (sec), leaf count = 501 {y(x)=_C12F1(12a(−a+d+a2+(−2d−4g)a+d2),−12a(a−d+a2+(−2d−4g)a+d2);12a2(d−4ac+b2a2a−2af+bd)1−4ac+b2a2;18ac−2b2((−2a2x−ab)−4ac+b2a2+4ac−b2))+_C2(2−4ac+b2a2xa2+−4ac+b2a2ba−4ac+b2)1a2(a(a−d2)−4ac+b2a2+af−bd2)1−4ac+b2a22F1(12a2(a(a+a2+(−2d−4g)a+d2)−4ac+b2a2+2af−bd)1−4ac+b2a2,12a2(a(a−a2+(−2d−4g)a+d2)−4ac+b2a2+2af−bd)1−4ac+b2a2;12a2(4a2−4ac+b2a2−d−4ac+b2a2a+2af−bd)1−4ac+b2a2;18ac−2b2((−2a2x−ab)−4ac+b2a2+4ac−b2))}
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