2.1587   ODE No. 1587

\[ x^5 y^{(10)}(x)-a y(x)=0 \]

✓ Mathematica : cpu = 0.285128 (sec), leaf count = 492

DSolve[-(a*y[x]) + x^5*Derivative[10][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \frac {(-1)^{4/5} a^{9/5} c_1 x^9 \, _0F_9\left (;\frac {6}{5},\frac {7}{5},\frac {8}{5},\frac {9}{5},2,\frac {11}{5},\frac {12}{5},\frac {13}{5},\frac {14}{5};\frac {a x^5}{9765625}\right )}{3814697265625}+\frac {(-1)^{3/5} a^{8/5} c_3 x^8 \, _0F_9\left (;\frac {4}{5},\frac {6}{5},\frac {7}{5},\frac {8}{5},\frac {9}{5},2,\frac {11}{5},\frac {12}{5},\frac {13}{5};\frac {a x^5}{9765625}\right )}{152587890625}+\frac {(-1)^{2/5} a^{7/5} c_5 x^7 \, _0F_9\left (;\frac {3}{5},\frac {4}{5},\frac {6}{5},\frac {7}{5},\frac {8}{5},\frac {9}{5},2,\frac {11}{5},\frac {12}{5};\frac {a x^5}{9765625}\right )}{6103515625}+\frac {\sqrt [5]{-1} a^{6/5} c_7 x^6 \, _0F_9\left (;\frac {2}{5},\frac {3}{5},\frac {4}{5},\frac {6}{5},\frac {7}{5},\frac {8}{5},\frac {9}{5},2,\frac {11}{5};\frac {a x^5}{9765625}\right )}{244140625}+\frac {a c_9 x^5 \, _0F_9\left (;\frac {1}{5},\frac {2}{5},\frac {3}{5},\frac {4}{5},\frac {6}{5},\frac {7}{5},\frac {8}{5},\frac {9}{5},2;\frac {a x^5}{9765625}\right )}{9765625}+c_{10} G_{0,10}^{2,0}\left (\frac {a x^5}{9765625}|\begin {array}{c} 0,1,\frac {1}{5},\frac {2}{5},\frac {3}{5},\frac {4}{5},\frac {6}{5},\frac {7}{5},\frac {8}{5},\frac {9}{5} \\\end {array}\right )+c_8 G_{0,10}^{2,0}\left (\frac {a x^5}{9765625}|\begin {array}{c} \frac {1}{5},\frac {6}{5},0,\frac {2}{5},\frac {3}{5},\frac {4}{5},1,\frac {7}{5},\frac {8}{5},\frac {9}{5} \\\end {array}\right )+c_6 G_{0,10}^{2,0}\left (\frac {a x^5}{9765625}|\begin {array}{c} \frac {2}{5},\frac {7}{5},0,\frac {1}{5},\frac {3}{5},\frac {4}{5},1,\frac {6}{5},\frac {8}{5},\frac {9}{5} \\\end {array}\right )+c_4 G_{0,10}^{2,0}\left (\frac {a x^5}{9765625}|\begin {array}{c} \frac {3}{5},\frac {8}{5},0,\frac {1}{5},\frac {2}{5},\frac {4}{5},1,\frac {6}{5},\frac {7}{5},\frac {9}{5} \\\end {array}\right )+c_2 G_{0,10}^{2,0}\left (\frac {a x^5}{9765625}|\begin {array}{c} \frac {4}{5},\frac {9}{5},0,\frac {1}{5},\frac {2}{5},\frac {3}{5},1,\frac {6}{5},\frac {7}{5},\frac {8}{5} \\\end {array}\right )\right \}\right \}\]

✓ Maple : cpu = 0.745 (sec), leaf count = 154

dsolve(x^5*diff(diff(diff(diff(diff(diff(diff(diff(diff(diff(y(x),x),x),x),x),x),x),x),x),x),x)-a*y(x)=0,y(x))
 

\[y \left (x \right ) = x^{{5}/{2}} \left (c_{10} \operatorname {BesselY}\left (5, 2 \left (-1\right )^{{9}/{10}} a^{{1}/{10}} \sqrt {x}\right )+c_{9} \operatorname {BesselY}\left (5, 2 \left (-1\right )^{{7}/{10}} a^{{1}/{10}} \sqrt {x}\right )+c_{8} \operatorname {BesselY}\left (5, 2 \left (-1\right )^{{3}/{10}} a^{{1}/{10}} \sqrt {x}\right )+c_{2} \operatorname {BesselY}\left (5, 2 i a^{{1}/{10}} \sqrt {x}\right )+c_{7} \operatorname {BesselY}\left (5, 2 \left (-1\right )^{{1}/{10}} a^{{1}/{10}} \sqrt {x}\right )+c_{6} \operatorname {BesselJ}\left (5, 2 \left (-1\right )^{{9}/{10}} a^{{1}/{10}} \sqrt {x}\right )+c_{5} \operatorname {BesselJ}\left (5, 2 \left (-1\right )^{{7}/{10}} a^{{1}/{10}} \sqrt {x}\right )+c_{4} \operatorname {BesselJ}\left (5, 2 \left (-1\right )^{{3}/{10}} a^{{1}/{10}} \sqrt {x}\right )+c_{3} \operatorname {BesselJ}\left (5, 2 \left (-1\right )^{{1}/{10}} a^{{1}/{10}} \sqrt {x}\right )+c_{1} \operatorname {BesselI}\left (5, 2 a^{{1}/{10}} \sqrt {x}\right )\right )\]