ODE No. 1500

2.1500 ODE No. 1500

Problem in Latex
Mathematica input
Maple input

$ν (2 x + 1) y^{'} (x) - ν (x + 1) y (x) - x (v + x) y^{″} (x) + x^{2} y^{(3)} (x) = 0$ ✗ Mathematica : cpu = 54.8371 (sec), leaf count = 0 , DiﬀerentialRoot result

$\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{\unicode {f818}^{(3)}(\unicode {f817}) \unicode {f817}^2-(\unicode {f817}+v) \unicode {f818}''(\unicode {f817}) \unicode {f817}-(\unicode {f817}+1) \nu \unicode {f818}(\unicode {f817})+(2 \unicode {f817} \nu +\nu ) \unicode {f818}'(\unicode {f817})=0,\unicode {f818}(1)=c_1,\unicode {f818}'(1)=c_2,\unicode {f818}''(1)=c_3\right \}\right )(x)\right \}\right \}$

✓ Maple : cpu = 0.247 (sec), leaf count = 55

${y (x) = e^{x}_C 1 +_C 2 x^{\frac{ν}{2} + \frac{1}{2}} J_{- ν - 1} (2 \sqrt{ν} \sqrt{x}) +_C 3 x^{\frac{ν}{2} + \frac{1}{2}} Y_{- ν - 1} (2 \sqrt{ν} \sqrt{x})}$

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