40.6.12 problem 12

Internal problem ID [8644]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 6. Laplace Transforms. Problem set 6.2, page 216
Problem number : 12
Date solved : Tuesday, September 30, 2025 at 05:40:08 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (4\right )&=-3 \\ y^{\prime }\left (4\right )&=-17 \\ \end{align*}

✓ Maple. Time used: 0.105 (sec). Leaf size: 21

ode:=diff(diff(y(t),t),t)-2*diff(y(t),t)-3*y(t) = 0; 
ic:=[y(4) = -3, D(y)(4) = -17]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = 2 \,{\mathrm e}^{-t +4}-5 \,{\mathrm e}^{3 t -12} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 24

ode=D[y[t],{t,2}]-2*D[y[t],t]-3*y[t]==0; 
ic={y[4]==-3,Derivative[1][y][4]==-17}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 2 e^{4-t}-5 e^{3 (t-4)} \end{align*}

✓ Sympy. Time used: 0.103 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-3*y(t) - 2*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(4): -3, Subs(Derivative(y(t), t), t, 4): -17} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - \frac {5 e^{3 t}}{e^{12}} + 2 e^{4} e^{- t} \]