66.2.13 problem Problem 13

Internal problem ID [13912]
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
Date solved : Tuesday, January 28, 2025 at 06:08:23 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} x^{\left (6\right )}-x^{\prime \prime \prime \prime }&=1 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 36

dsolve(diff(x(t),t$6)-diff(x(t),t$4)=1,x(t), singsol=all)
 

\[ x \left (t \right ) = -\frac {t^{4}}{24}+{\mathrm e}^{-t} c_{1} +\frac {c_{3} t^{3}}{6}+\frac {c_4 \,t^{2}}{2}+c_{2} {\mathrm e}^{t}+c_5 t +c_6 \]

✓ Solution by Mathematica

Time used: 0.065 (sec). Leaf size: 45

DSolve[D[x[t],{t,6}]-D[x[t],{t,4}]==1,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to -\frac {t^4}{24}+c_6 t^3+c_5 t^2+c_4 t+c_1 e^t+c_2 e^{-t}+c_3 \]