68.13.36 problem 63 (a)

Internal problem ID [17689]
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 : 63 (a)
Date solved : Thursday, October 02, 2025 at 02:27:03 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+6 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 )&=-1 \\ \end{align*}

✓ Maple. Time used: 0.106 (sec). Leaf size: 30

ode:=diff(diff(diff(y(t),t),t),t)+3*diff(diff(y(t),t),t)+2*diff(y(t),t)+6*y(t) = 0; 
ic:=[y(0) = 0, D(y)(0) = 1, (D@@2)(y)(0) = -1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{-3 t}}{11}+\frac {4 \sqrt {2}\, \sin \left (\sqrt {2}\, t \right )}{11}+\frac {\cos \left (\sqrt {2}\, t \right )}{11} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 40

ode=D[ y[t],{t,3}]+3*D[y[t],{t,2}]+2*D[y[t],t]+6*y[t]==0; 
ic={y[0]==0,Derivative[1][y][0] ==1,Derivative[2][y][0] ==-1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{11} \left (-e^{-3 t}+4 \sqrt {2} \sin \left (\sqrt {2} t\right )+\cos \left (\sqrt {2} t\right )\right ) \end{align*}

✓ Sympy. Time used: 0.134 (sec). Leaf size: 37

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(6*y(t) + 2*Derivative(y(t), t) + 3*Derivative(y(t), (t, 2)) + 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): -1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {4 \sqrt {2} \sin {\left (\sqrt {2} t \right )}}{11} + \frac {\cos {\left (\sqrt {2} t \right )}}{11} - \frac {e^{- 3 t}}{11} \]