67.3.7 problem Problem 8

Internal problem ID [13954]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 5.5 Laplace transform. Homogeneous equations. Problems page 357
Problem number : Problem 8
Date solved : Monday, March 31, 2025 at 08:20:11 AM
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 )&=2\\ y^{\prime }\left (0\right )&=3 \end{align*}

✓ Maple. Time used: 0.090 (sec). Leaf size: 17

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

\[ y = 7 \,{\mathrm e}^{-t}-5 \,{\mathrm e}^{-2 t} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 18

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

\[ y(t)\to e^{-2 t} \left (7 e^t-5\right ) \]

✓ Sympy. Time used: 0.207 (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): 2, Subs(Derivative(y(t), t), t, 0): 3} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (7 - 5 e^{- t}\right ) e^{- t} \]