46.6.3 problem 23

Internal problem ID [9624]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 7 THE LAPLACE TRANSFORM. 7.3.1 TRANSLATION ON THE s-AXIS. Page 297
Problem number : 23
Date solved : Tuesday, September 30, 2025 at 06:21:35 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+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: 0.090 (sec). Leaf size: 14

ode:=diff(diff(y(t),t),t)+2*diff(y(t),t)+y(t) = 0; 
ic:=[y(0) = 1, D(y)(0) = 1]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = \left (2 t +1\right ) {\mathrm e}^{-t} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 16

ode=D[y[t],{t,2}]+2*D[y[t],t]+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} (2 t+1) \end{align*}

✓ Sympy. Time used: 0.091 (sec). Leaf size: 10

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): 1, Subs(Derivative(y(t), t), t, 0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (2 t + 1\right ) e^{- t} \]