68.14.24 problem 24

Internal problem ID [17716]
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 : 24
Date solved : Thursday, October 02, 2025 at 02:27:18 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (6\right )}+y^{\prime \prime \prime \prime }&=-24 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 34

ode:=diff(diff(diff(diff(diff(diff(y(t),t),t),t),t),t),t)+diff(diff(diff(diff(y(t),t),t),t),t) = -24; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {c_3 \,t^{3}}{6}-t^{4}+\cos \left (t \right ) c_1 +\sin \left (t \right ) c_2 +\frac {c_4 \,t^{2}}{2}+c_5 t +c_6 \]

✓ Mathematica. Time used: 60.019 (sec). Leaf size: 67

ode=D[ y[t],{t,6}]+D[y[t],{t,4}]==-24; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \int _1^t\int _1^{K[4]}\int _1^{K[3]}\int _1^{K[2]}(c_1 \cos (K[1])+c_2 \sin (K[1])-24)dK[1]dK[2]dK[3]dK[4]+t (t (c_6 t+c_5)+c_4)+c_3 \end{align*}

✓ Sympy. Time used: 0.048 (sec). Leaf size: 31

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), (t, 4)) + Derivative(y(t), (t, 6)) + 24,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} + C_{2} t + C_{3} t^{2} + C_{4} t^{3} + C_{5} \sin {\left (t \right )} + C_{6} \cos {\left (t \right )} - t^{4} \]