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y″(x)=−y′(x)(−x(a(δ+gamma1)+α+β−δ+1)+agamma1+x2(α+β+1))(x−1)x(x−a)−y(x)(αβx−q)(x−1)x(x−a) ✗ Mathematica : cpu = 6.43599 (sec), leaf count = 0 , DifferentialRoot result
\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{(\unicode {f817} \alpha \beta -q) \unicode {f818}(\unicode {f817})+\left (\alpha \unicode {f817}^2+\beta \unicode {f817}^2+\unicode {f817}^2-\alpha \unicode {f817}-\beta \unicode {f817}-a \delta \unicode {f817}+\delta \unicode {f817}-a \text {gamma1} \unicode {f817}-\unicode {f817}+a \text {gamma1}\right ) \unicode {f818}'(\unicode {f817})-(\unicode {f817}-1) \unicode {f817} (a-\unicode {f817}) \unicode {f818}''(\unicode {f817})=0,\unicode {f818}(2)=c_1,\unicode {f818}'(2)=c_2\right \}\right )(x)\right \}\right \}\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{(\unicode {f817} \alpha \beta -q) \unicode {f818}(\unicode {f817})+\left (\alpha \unicode {f817}^2+\beta \unicode {f817}^2+\unicode {f817}^2-\alpha \unicode {f817}-\beta \unicode {f817}-a \delta \unicode {f817}+\delta \unicode {f817}-a \text {gamma1} \unicode {f817}-\unicode {f817}+a \text {gamma1}\right ) \unicode {f818}'(\unicode {f817})-(\unicode {f817}-1) \unicode {f817} (a-\unicode {f817}) \unicode {f818}''(\unicode {f817})=0,\unicode {f818}(2)=c_1,\unicode {f818}'(2)=c_2\right \}\right )(x)\right \}\right \}
✓ Maple : cpu = 0.365 (sec), leaf count = 64
{y(x)=_C1HeunG(a,q,α,β,γ1,δ,x)+_C2x1−γ1HeunG(a,q−(−1+γ1)(δ(a−1)+α+β−γ1+1),β+1−γ1,α+1−γ1,−γ1+2,δ,x)}
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