90.29.6 problem 23

Internal problem ID [25438]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 6. Discontinuous Functions and the Laplace Transform. Exercises at page 449
Problem number : 23
Date solved : Friday, October 03, 2025 at 12:01:32 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=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: 0.038 (sec). Leaf size: 12

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

\[ y = \left (-5 t +2\right ) {\mathrm e}^{t} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 14

ode=D[y[t],{t,2}]-2*D[y[t],t]+y[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^t (2-5 t) \end{align*}

✓ Sympy. Time used: 0.098 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) - 2*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)
 

\[ y{\left (t \right )} = \left (2 - 5 t\right ) e^{t} \]