40.6.3 problem 3

Internal problem ID [8635]
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 : 3
Date solved : Tuesday, September 30, 2025 at 05:40:04 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=11 \\ y^{\prime }\left (0\right )&=28 \\ \end{align*}

✓ Maple. Time used: 0.104 (sec). Leaf size: 15

ode:=diff(diff(y(t),t),t)-diff(y(t),t)-6*y(t) = 0; 
ic:=[y(0) = 11, D(y)(0) = 28]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = 10 \,{\mathrm e}^{3 t}+{\mathrm e}^{-2 t} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 18

ode=D[y[t],{t,2}]-D[y[t],t]-6*y[t]==0; 
ic={y[0]==11,Derivative[1][y][0] ==28}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-2 t}+10 e^{3 t} \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-6*y(t) - Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 11, Subs(Derivative(y(t), t), t, 0): 28} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 10 e^{3 t} + e^{- 2 t} \]