65.6.9 problem 12.1 (ix)

Internal problem ID [13687]
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 (ix)
Date solved : Monday, March 31, 2025 at 08:08:58 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Maple. Time used: 0.041 (sec). Leaf size: 11

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

\[ y = -{\mathrm e}^{-t} t \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 13

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

\[ y(t)\to -e^{-t} t \]

✓ Sympy. Time used: 0.149 (sec). Leaf size: 8

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

\[ y{\left (t \right )} = - t e^{- t} \]