60.6.5 problem 1582
Internal
problem
ID
[11542]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
5,
linear
fifth
and
higher
order
Problem
number
:
1582
Date
solved
:
Sunday, March 30, 2025 at 08:24:34 PM
CAS
classification
:
[[_high_order, _with_linear_symmetries]]
\begin{align*} y^{\left (5\right )}+a \,x^{\nu } y^{\prime }+a \nu \,x^{\nu -1} y&=0 \end{align*}
✗ Maple
ode:=diff(diff(diff(diff(diff(y(x),x),x),x),x),x)+a*x^nu*diff(y(x),x)+a*nu*x^(nu-1)*y(x) = 0;
dsolve(ode,y(x), singsol=all);
\[ \text {No solution found} \]
✓ Mathematica. Time used: 10.105 (sec). Leaf size: 528
ode=D[y[x],{x,5}]+a*x^\[Nu]*D[y[x],x]+a*\[Nu]*x^(\[Nu]-1)*y[x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
y(x)\to \nu ^{-\frac {16}{\nu +4}} \left (\frac {\nu +4}{\nu }\right )^{-\frac {16}{\nu +4}} a^{\frac {1}{\nu +4}} \left (x^{\nu }\right )^{\frac {1}{\nu }} \left (a^{\frac {1}{\nu +4}} \left (x^{\nu }\right )^{\frac {1}{\nu }} \left (a^{\frac {1}{\nu +4}} \left (x^{\nu }\right )^{\frac {1}{\nu }} \left (c_5 a^{\frac {1}{\nu +4}} \left (x^{\nu }\right )^{\frac {1}{\nu }} \, _1F_4\left (1;\frac {\nu }{\nu +4}+\frac {5}{\nu +4},\frac {\nu }{\nu +4}+\frac {6}{\nu +4},\frac {\nu }{\nu +4}+\frac {7}{\nu +4},\frac {\nu }{\nu +4}+\frac {8}{\nu +4};-\frac {a \left (x^{\nu }\right )^{\frac {\nu +4}{\nu }}}{(\nu +4)^4}\right )+c_4 \nu ^{\frac {4}{\nu +4}} \left (\frac {\nu +4}{\nu }\right )^{\frac {4}{\nu +4}} \, _0F_3\left (;\frac {\nu }{\nu +4}+\frac {5}{\nu +4},\frac {\nu }{\nu +4}+\frac {6}{\nu +4},\frac {\nu }{\nu +4}+\frac {7}{\nu +4};-\frac {a \left (x^{\nu }\right )^{\frac {\nu +4}{\nu }}}{(\nu +4)^4}\right )\right )+c_3 \nu ^{\frac {8}{\nu +4}} \left (\frac {\nu +4}{\nu }\right )^{\frac {8}{\nu +4}} \, _0F_3\left (;\frac {\nu }{\nu +4}+\frac {3}{\nu +4},\frac {\nu }{\nu +4}+\frac {5}{\nu +4},\frac {\nu }{\nu +4}+\frac {6}{\nu +4};-\frac {a \left (x^{\nu }\right )^{\frac {\nu +4}{\nu }}}{(\nu +4)^4}\right )\right )+c_2 \nu ^{\frac {12}{\nu +4}} \left (\frac {\nu +4}{\nu }\right )^{\frac {12}{\nu +4}} \, _0F_3\left (;\frac {\nu }{\nu +4}+\frac {2}{\nu +4},\frac {\nu }{\nu +4}+\frac {3}{\nu +4},\frac {\nu }{\nu +4}+\frac {5}{\nu +4};-\frac {a \left (x^{\nu }\right )^{\frac {\nu +4}{\nu }}}{(\nu +4)^4}\right )\right )+c_1 \, _0F_3\left (;\frac {\nu }{\nu +4}+\frac {1}{\nu +4},\frac {\nu }{\nu +4}+\frac {2}{\nu +4},\frac {\nu }{\nu +4}+\frac {3}{\nu +4};-\frac {a \left (x^{\nu }\right )^{\frac {\nu +4}{\nu }}}{(\nu +4)^4}\right )
\]
✗ Sympy
from sympy import *
x = symbols("x")
a = symbols("a")
nu = symbols("nu")
y = Function("y")
ode = Eq(a*nu*x**(nu - 1)*y(x) + a*x**nu*Derivative(y(x), x) + Derivative(y(x), (x, 5)),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
RecursionError : maximum recursion depth exceeded