ODE No. 1520

2.1520 ODE No. 1520

Problem in Latex
Mathematica input
Maple input

$y^{″} (x) (- 6 x (a1 + a2 + a3) + 3 a1 a2 + 3 a1 a3 + 3 a2 a3 + 9 x^{2}) + 2 (x - a1) (x - a2) (x - a3) y^{(3)} (x) - 2 (b + (n^{2} + n - 3) x) y^{'} (x) - n (n + 1) y (x) = 0$ ✗ Mathematica : cpu = 66.496 (sec), leaf count = 0 , DiﬀerentialRoot result

$\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{-n (n+1) \unicode {f818}(\unicode {f817})-2 \left (\unicode {f817} n^2+\unicode {f817} n-3 \unicode {f817}+b\right ) \unicode {f818}'(\unicode {f817})+3 \left (3 \unicode {f817}^2-2 \text {a1} \unicode {f817}-2 \text {a2} \unicode {f817}-2 \text {a3} \unicode {f817}+\text {a1} \text {a2}+\text {a1} \text {a3}+\text {a2} \text {a3}\right ) \unicode {f818}''(\unicode {f817})-2 (\text {a1}-\unicode {f817}) (\text {a2}-\unicode {f817}) (\text {a3}-\unicode {f817}) \unicode {f818}^{(3)}(\unicode {f817})=0,\unicode {f818}(0)=c_1,\unicode {f818}'(0)=c_2,\unicode {f818}''(0)=c_3\right \},\langle \langle \rangle \rangle \right )(x)\right \}\right \}$

✓ Maple : cpu = 2.532 (sec), leaf count = 272

${y (x) =_C 1 {(H e u n G (\frac{a 1 - a 3}{a 2 - a 3}, \frac{(n^{2} + n - 1) a 3 + b - a 1 - a 2}{4 a 2 - 4 a 3}, - \frac{n}{2}, \frac{n}{2} + \frac{1}{2}, \frac{1}{2}, \frac{1}{2}, \frac{x - a 3}{a 2 - a 3}))}^{2} +_C 3 H e u n G (\frac{a 1 - a 3}{a 2 - a 3}, \frac{(n^{2} + n - 1) a 3 + b - a 1 - a 2}{4 a 2 - 4 a 3}, - \frac{n}{2}, \frac{n}{2} + \frac{1}{2}, \frac{1}{2}, \frac{1}{2}, \frac{x - a 3}{a 2 - a 3}) H e u n G (\frac{a 1 - a 3}{a 2 - a 3}, \frac{(n^{2} + n - 3) a 3 + b}{4 a 2 - 4 a 3}, \frac{n}{2} + 1, - \frac{n}{2} + \frac{1}{2}, \frac{3}{2}, \frac{1}{2}, \frac{x - a 3}{a 2 - a 3}) \sqrt{- x + a 3} - {(H e u n G (\frac{a 1 - a 3}{a 2 - a 3}, \frac{(n^{2} + n - 3) a 3 + b}{4 a 2 - 4 a 3}, \frac{n}{2} + 1, - \frac{n}{2} + \frac{1}{2}, \frac{3}{2}, \frac{1}{2}, \frac{x - a 3}{a 2 - a 3}))}^{2}_C 2 (x - a 3)}$

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