90.29.7 problem 24

Internal problem ID [25439]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 6. Discontinuous Functions and the Laplace Transform. Exercises at page 449
Problem number : 24
Date solved : Friday, October 03, 2025 at 12:01:33 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=0 \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.036 (sec). Leaf size: 10

ode:=diff(diff(y(t),t),t)+4*diff(y(t),t)+3*y(t) = 0; 
ic:=[y(0) = -1, D(y)(0) = 1]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

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

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 12

ode=D[y[t],{t,2}]+4*D[y[t],t]+3*y[t]==0; 
ic={y[0]==-1,Derivative[1][y][0] ==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -e^{-t} \end{align*}

✓ Sympy. Time used: 0.115 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(3*y(t) + 4*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): -1, Subs(Derivative(y(t), t), t, 0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

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