Internal problem ID [9168]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 5, linear fifth and higher order
Problem number: 1589.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{\frac {5}{2}} y^{\relax (5)}-a y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.045 (sec). Leaf size: 2173
dsolve(x^(2+1/2)*diff(y(x),x$5)-a*y(x)=0,y(x), singsol=all)
\[ \text {Expression too large to display} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 206
DSolve[x^(2+1/2)*D[y[x],{x,5}]-a*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {4}{25} (-1)^{2/5} a^{2/5} c_2 x \, _0F_4\left (;-\frac {1}{5},\frac {1}{5},\frac {3}{5},\frac {7}{5};\frac {32 a x^{5/2}}{3125}\right )+\frac {16 \sqrt [5]{-1} a^{4/5} x^2 \left (625 (-1)^{3/5} c_3 \, _0F_4\left (;\frac {1}{5},\frac {3}{5},\frac {7}{5},\frac {9}{5};\frac {32 a x^{5/2}}{3125}\right )-4 a^{2/5} x \left (4 (-1)^{2/5} a^{2/5} c_5 x \, _0F_4\left (;\frac {7}{5},\frac {9}{5},\frac {11}{5},\frac {13}{5};\frac {32 a x^{5/2}}{3125}\right )+25 c_4 \, _0F_4\left (;\frac {3}{5},\frac {7}{5},\frac {9}{5},\frac {11}{5};\frac {32 a x^{5/2}}{3125}\right )\right )\right )}{390625}+c_1 \, _0F_4\left (;-\frac {3}{5},-\frac {1}{5},\frac {1}{5},\frac {3}{5};\frac {32 a x^{5/2}}{3125}\right ) \\ \end{align*}