83.15.2 problem 4 (b)

Internal problem ID [22026]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter XV. The Laplace Transform. Ex. XXIII at page 251
Problem number : 4 (b)
Date solved : Thursday, October 02, 2025 at 08:21:47 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }&=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: 0.037 (sec). Leaf size: 10

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

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

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 12

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

\begin{align*} y(t)&\to e^{-3 t}-3 \end{align*}

✓ Sympy. Time used: 0.090 (sec). Leaf size: 10

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

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