ODE No. 1586

7.13 ODE No. 1586

$x \frac{d^{5}}{d x^{5}} y (x) - (a A_{1} - A_{0}) x - A_{1} - ((a A_{2} - A_{1}) x + A_{2}) \frac{d}{d x} y (x) - ((a A_{3} - A_{2}) x + A_{3}) \frac{d^{2}}{d x^{2}} y (x) - ((a A_{4} - A_{3}) x + A_{4}) \frac{d^{3}}{d x^{3}} y (x) - ((a A_{5} - A_{4}) x + A_{5}) \frac{d^{4}}{d x^{4}} y (x) = 0$

Mathematica: cpu = 84.450724 (sec), leaf count = 148 $\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{\unicode {f817} A(0)-\unicode {f817} a A(1)-A(1)+(\unicode {f817} A(1)-\unicode {f817} a A(2)-A(2)) \unicode {f818}'(\unicode {f817})+(\unicode {f817} A(2)-\unicode {f817} a A(3)-A(3)) \unicode {f818}''(\unicode {f817})+(\unicode {f817} A(3)-\unicode {f817} a A(4)-A(4)) \unicode {f818}^{(3)}(\unicode {f817})+(\unicode {f817} A(4)-\unicode {f817} a A(5)-A(5)) \unicode {f818}^{(4)}(\unicode {f817})+\unicode {f817} \unicode {f818}^{(5)}(\unicode {f817})=0,\unicode {f818}(1)=c_1,\unicode {f818}'(1)=c_2,\unicode {f818}''(1)=c_3,\unicode {f818}^{(3)}(1)=c_4,\unicode {f818}^{(4)}(1)=c_5\right \}\right )(x)\right \}\right \}$

Maple: cpu = 0.124 (sec), leaf count = 119 ${y (x) = \int D E S o l ({- \frac{(a x A_{2} - x A_{1} + A_{2})_Y (x)}{x} - \frac{(a x A_{3} - x A_{2} + A_{3}) \frac{d}{d x}_Y (x)}{x} - \frac{(a x A_{4} - x A_{3} + A_{4}) \frac{d^{2}}{d x^{2}}_Y (x)}{x} - \frac{(a x A_{5} - x A_{4} + A_{5}) \frac{d^{3}}{d x^{3}}_Y (x)}{x} + \frac{d^{4}}{d x^{4}}_Y (x) - \frac{a x A_{1} - x A_{0} + A_{1}}{x}}, {_Y (x)}) d x +_C 1}$

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