60.6.12 problem 1589

Internal problem ID [11549]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 5, linear fifth and higher order
Problem number : 1589
Date solved : Sunday, March 30, 2025 at 08:24:41 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} x^{{5}/{2}} y^{\left (5\right )}-a y&=0 \end{align*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 492

ode:=x^(5/2)*diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-a*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {Expression too large to display} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 206

ode=x^(2+1/2)*D[y[x],{x,5}]-a*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {4}{25} (-1)^{2/5} a^{2/5} c_2 x \, _0F_4\left (;-\frac {1}{5},\frac {1}{5},\frac {3}{5},\frac {7}{5};\frac {32 a x^{5/2}}{3125}\right )+\frac {16 \sqrt [5]{-1} a^{4/5} x^2 \left (625 (-1)^{3/5} c_3 \, _0F_4\left (;\frac {1}{5},\frac {3}{5},\frac {7}{5},\frac {9}{5};\frac {32 a x^{5/2}}{3125}\right )-4 a^{2/5} x \left (4 (-1)^{2/5} a^{2/5} c_5 x \, _0F_4\left (;\frac {7}{5},\frac {9}{5},\frac {11}{5},\frac {13}{5};\frac {32 a x^{5/2}}{3125}\right )+25 c_4 \, _0F_4\left (;\frac {3}{5},\frac {7}{5},\frac {9}{5},\frac {11}{5};\frac {32 a x^{5/2}}{3125}\right )\right )\right )}{390625}+c_1 \, _0F_4\left (;-\frac {3}{5},-\frac {1}{5},\frac {1}{5},\frac {3}{5};\frac {32 a x^{5/2}}{3125}\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-a*y(x) + x**(5/2)*Derivative(y(x), (x, 5)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve -a*y(x) + x**(5/2)*Derivative(y(x), (x, 5))