65.6.7 problem 12.1 (vii)

Internal problem ID [13677]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 12, Homogeneous second order linear equations. Exercises page 118
Problem number : 12.1 (vii)
Date solved : Wednesday, March 05, 2025 at 10:11:40 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 20

ode:=diff(diff(y(t),t),t)+2*diff(y(t),t)+10*y(t) = 0; 
ic:=y(0) = 3, D(y)(0) = 0; 
dsolve([ode,ic],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 22

ode=D[y[t],{t,2}]+2*D[y[t],t]+10*y[t]==0; 
ic={y[0]==3,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-t} (\sin (3 t)+3 \cos (3 t)) \]

✓ Sympy. Time used: 0.160 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(10*y(t) + 2*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 3, Subs(Derivative(y(t), t), t, 0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

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