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(−2(x2−1)(μ(μ+1)+ν(ν+1))+24x3−8)y″(x)−6x(μ(μ+1)+ν(ν+1)−2)y′(x)+((μ(μ+1)−ν(ν+1))2−2μ(μ+1)−2ν(ν+1))y(x)+(x2−1)2y(4)(x)+10x(x2−1)y(3)(x)=0 ✗ Mathematica : cpu = 93.2549 (sec), leaf count = 0 , DifferentialRoot result
\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{(\mu -\nu -1) (\mu -\nu +1) (\mu +\nu ) (\mu +\nu +2) \unicode {f818}(\unicode {f817})-6 \unicode {f817} \left (\mu ^2+\mu +\nu ^2+\nu -2\right ) \unicode {f818}'(\unicode {f817})-2 \left (-12 \unicode {f817}^3+\mu ^2 \unicode {f817}^2+\nu ^2 \unicode {f817}^2+\mu \unicode {f817}^2+\nu \unicode {f817}^2-\mu ^2-\nu ^2-\mu -\nu +4\right ) \unicode {f818}''(\unicode {f817})+\left (10 \unicode {f817}^3-10 \unicode {f817}\right ) \unicode {f818}^{(3)}(\unicode {f817})+\left (\unicode {f817}^4-2 \unicode {f817}^2+1\right ) \unicode {f818}^{(4)}(\unicode {f817})=0,\unicode {f818}(0)=c_1,\unicode {f818}'(0)=c_2,\unicode {f818}''(0)=c_3,\unicode {f818}^{(3)}(0)=c_4\right \},\langle \langle \rangle \rangle \right )(x)\right \}\right \}\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{(\mu -\nu -1) (\mu -\nu +1) (\mu +\nu ) (\mu +\nu +2) \unicode {f818}(\unicode {f817})-6 \unicode {f817} \left (\mu ^2+\mu +\nu ^2+\nu -2\right ) \unicode {f818}'(\unicode {f817})-2 \left (-12 \unicode {f817}^3+\mu ^2 \unicode {f817}^2+\nu ^2 \unicode {f817}^2+\mu \unicode {f817}^2+\nu \unicode {f817}^2-\mu ^2-\nu ^2-\mu -\nu +4\right ) \unicode {f818}''(\unicode {f817})+\left (10 \unicode {f817}^3-10 \unicode {f817}\right ) \unicode {f818}^{(3)}(\unicode {f817})+\left (\unicode {f817}^4-2 \unicode {f817}^2+1\right ) \unicode {f818}^{(4)}(\unicode {f817})=0,\unicode {f818}(0)=c_1,\unicode {f818}'(0)=c_2,\unicode {f818}''(0)=c_3,\unicode {f818}^{(3)}(0)=c_4\right \},\langle \langle \rangle \rangle \right )(x)\right \}\right \}
✓ Maple : cpu = 0.464 (sec), leaf count = 35
{y(x)=(LegendreQ(μ,x)_C2+_C1LegendreP(μ,x))LegendreP(ν,x)+LegendreQ(ν,x)(LegendreQ(μ,x)_C4+_C3LegendreP(μ,x))}
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