Internal problem ID [10828]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER.
Problems page 172
Problem number: Problem 13.
ODE order: 6.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {x^{\left (6\right )}-x^{\prime \prime \prime \prime }-1=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(diff(x(t),t$6)-diff(x(t),t$4)=1,x(t), singsol=all)
\[ x \left (t \right ) = -\frac {t^{4}}{24}+{\mathrm e}^{t} c_{1} +\frac {c_{3} t^{3}}{6}+\frac {t^{2} c_{4}}{2}+{\mathrm e}^{-t} c_{2} +c_{5} t +c_{6} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 45
DSolve[x''''''[t]-x''''[t]==1,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {t^4}{24}+c_6 t^3+c_5 t^2+c_4 t+c_1 e^t+c_2 e^{-t}+c_3 \\ \end{align*}