40.7.1 problem 18

Internal problem ID [8648]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 6. Laplace Transforms. Problem set 6.3, page 224
Problem number : 18
Date solved : Tuesday, September 30, 2025 at 05:40:10 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime }-6 y^{\prime }+y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=3 \\ y^{\prime }\left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.093 (sec). Leaf size: 10

ode:=9*diff(diff(y(t),t),t)-6*diff(y(t),t)+y(t) = 0; 
ic:=[y(0) = 3, D(y)(0) = 1]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 14

ode=9*D[y[t],{t,2}]-6*D[y[t],t]+y[t]==0; 
ic={y[0]==3,Derivative[1][y][0] ==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.098 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) - 6*Derivative(y(t), t) + 9*Derivative(y(t), (t, 2)),0) 
ics = {y(0): 3, Subs(Derivative(y(t), t), t, 0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

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