74.13.34 problem 58

Internal problem ID [16321]
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 : 58
Date solved : Thursday, March 13, 2025 at 08:10:24 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+9 y^{\prime \prime }+16 y^{\prime }-26 y&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 24

ode:=diff(diff(diff(y(t),t),t),t)+9*diff(diff(y(t),t),t)+16*diff(y(t),t)-26*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

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

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

ode=D[ y[t],{t,3}]+9*D[y[t],{t,2}]+16*D[y[t],t]-26*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-5 t} \left (c_3 e^{6 t}+c_2 \cos (t)+c_1 \sin (t)\right ) \]

✓ Sympy. Time used: 0.204 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-26*y(t) + 16*Derivative(y(t), t) + 9*Derivative(y(t), (t, 2)) + Derivative(y(t), (t, 3)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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