Internal problem ID [9161]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 5, linear fifth and higher order
Problem number: 1582.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\relax (5)}+a \,x^{\nu } y^{\prime }+a \nu \,x^{\nu -1} y=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(y(x),x$5)+a*x^nu*diff(y(x),x)+a*nu*x^(nu-1)*y(x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 10.105 (sec). Leaf size: 496
DSolve[y'''''[x]+a*x^\[Nu]*y'[x]+a*\[Nu]*x^(\[Nu]-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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;1+\frac {1}{\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 (;1+\frac {1}{\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 (;1+\frac {1}{\nu +4},\frac {\nu }{\nu +4}+\frac {3}{\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 (;1+\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 )\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 ) \\ \end{align*}