68.14.3 problem 3

Internal problem ID [17695]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.6, page 187
Problem number : 3
Date solved : Thursday, October 02, 2025 at 02:27:07 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }&=1 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 30

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

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

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 37

ode=D[ y[t],{t,5}]-D[y[t],{t,4}]==1; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\frac {t^4}{24}+c_5 t^3+c_4 t^2+c_3 t+c_1 e^t+c_2 \end{align*}

✓ Sympy. Time used: 0.050 (sec). Leaf size: 27

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-Derivative(y(t), (t, 4)) + Derivative(y(t), (t, 5)) - 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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