Internal problem ID [9162]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 5, linear fifth and higher order
Problem number: 1583.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\relax (5)}+a y^{\prime \prime \prime \prime }-f=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 40
dsolve(diff(y(x),x$5)+a*diff(y(x),x$4)-f=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2} c_{3}}{2}+\frac {x^{3} c_{2}}{6}+\frac {c_{1} {\mathrm e}^{-a x}}{a^{4}}+\frac {f \,x^{4}}{24 a}+c_{4} x +c_{5} \]
✓ Solution by Mathematica
Time used: 0.173 (sec). Leaf size: 45
DSolve[y'''''[x]+a*y''''[x]-f==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 e^{-a x}}{a^4}+\frac {f x^4}{24 a}+x (x (c_5 x+c_4)+c_3)+c_2 \\ \end{align*}