40.6.8 problem 8

Internal problem ID [8640]
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 : 8
Date solved : Tuesday, September 30, 2025 at 05:40:06 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&={\frac {81}{10}} \\ y^{\prime }\left (0\right )&={\frac {39}{10}} \\ \end{align*}

✓ Maple. Time used: 0.099 (sec). Leaf size: 15

ode:=diff(diff(y(t),t),t)-4*diff(y(t),t)+4*y(t) = 0; 
ic:=[y(0) = 81/10, D(y)(0) = 39/10]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = -\frac {3 \left (41 t -27\right ) {\mathrm e}^{2 t}}{10} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 19

ode=D[y[t],{t,2}]-4*D[y[t],t]+4*y[t]==0; 
ic={y[0]==81/10,Derivative[1][y][0] ==39/10}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\frac {3}{10} e^{2 t} (41 t-27) \end{align*}

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

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*y(t) - 4*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 81/10, Subs(Derivative(y(t), t), t, 0): 39/10} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (\frac {81}{10} - \frac {123 t}{10}\right ) e^{2 t} \]