66.2.13 problem Problem 13

Internal problem ID [13841]
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 : Monday, March 31, 2025 at 08:14:53 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 36

ode:=diff(diff(diff(diff(diff(diff(x(t),t),t),t),t),t),t)-diff(diff(diff(diff(x(t),t),t),t),t) = 1; 
dsolve(ode,x(t), singsol=all);
 

\[ x = -\frac {t^{4}}{24}+\frac {c_3 \,t^{3}}{6}+\frac {c_4 \,t^{2}}{2}+{\mathrm e}^{t} c_1 +{\mathrm e}^{-t} c_2 +c_5 t +c_6 \]

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

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

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

✓ Sympy. Time used: 0.126 (sec). Leaf size: 32

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-Derivative(x(t), (t, 4)) + Derivative(x(t), (t, 6)) - 1,0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = C_{1} + C_{2} t + C_{3} t^{2} + C_{4} t^{3} + C_{5} e^{- t} + C_{6} e^{t} - \frac {t^{4}}{24} \]