68.13.18 problem 35

Internal problem ID [17671]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.5, page 175
Problem number : 35
Date solved : Thursday, October 02, 2025 at 02:26:58 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

ode:=diff(diff(diff(diff(diff(y(t),t),t),t),t),t)+3*diff(diff(diff(diff(y(t),t),t),t),t)+3*diff(diff(diff(y(t),t),t),t)+diff(diff(y(t),t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (c_5 \,t^{2}+c_4 t +c_3 \right ) {\mathrm e}^{-t}+c_2 t +c_1 \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 48

ode=D[ y[t],{t,5}]+3*D[y[t],{t,4}]+3*D[ y[t],{t,3}]+D[y[t],{t,2}]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.061 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), (t, 2)) + 3*Derivative(y(t), (t, 3)) + 3*Derivative(y(t), (t, 4)) + Derivative(y(t), (t, 5)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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