87.22.6 problem 6

Internal problem ID [23751]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 4. The Laplace transform. Exercise at page 199
Problem number : 6
Date solved : Thursday, October 02, 2025 at 09:44:53 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 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: 0.044 (sec). Leaf size: 17

ode:=diff(diff(y(t),t),t)+3*diff(y(t),t)+2*y(t) = 0; 
ic:=[y(0) = 1, D(y)(0) = 1]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = 3 \,{\mathrm e}^{-t}-2 \,{\mathrm e}^{-2 t} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 18

ode=D[y[t],{t,2}]+3*D[y[t],t]+2*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^{-2 t} \left (3 e^t-2\right ) \end{align*}

✓ Sympy. Time used: 0.124 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*y(t) + 3*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)
 

\[ y{\left (t \right )} = \left (3 - 2 e^{- t}\right ) e^{- t} \]