68.13.27 problem 44

Internal problem ID [17680]
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 : 44
Date solved : Thursday, October 02, 2025 at 02:27:00 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 24 y^{\prime \prime \prime }-26 y^{\prime \prime }+9 y^{\prime }-y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ y^{\prime }\left (0\right )&=1 \\ y^{\prime \prime }\left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.056 (sec). Leaf size: 23

ode:=24*diff(diff(diff(y(t),t),t),t)-26*diff(diff(y(t),t),t)+9*diff(y(t),t)-y(t) = 0; 
ic:=[y(0) = 0, D(y)(0) = 1, (D@@2)(y)(0) = 0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = -14 \,{\mathrm e}^{\frac {t}{2}}+54 \,{\mathrm e}^{\frac {t}{3}}-40 \,{\mathrm e}^{\frac {t}{4}} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 33

ode=24*D[ y[t],{t,3}]-26*D[y[t],{t,2}]+9*D[y[t],t]-y[t]==0; 
ic={y[0]==0,Derivative[1][y][0] ==1,Derivative[2][y][0] ==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -40 e^{t/4}+54 e^{t/3}-14 e^{t/2} \end{align*}

✓ Sympy. Time used: 0.130 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t) + 9*Derivative(y(t), t) - 26*Derivative(y(t), (t, 2)) + 24*Derivative(y(t), (t, 3)),0) 
ics = {y(0): 0, Subs(Derivative(y(t), t), t, 0): 1, Subs(Derivative(y(t), (t, 2)), t, 0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - 40 e^{\frac {t}{4}} + 54 e^{\frac {t}{3}} - 14 e^{\frac {t}{2}} \]