68.10.24 problem 24

Internal problem ID [17516]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.2, page 147
Problem number : 24
Date solved : Thursday, October 02, 2025 at 02:25:00 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=4 \\ y^{\prime }\left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.050 (sec). Leaf size: 11

ode:=diff(diff(y(t),t),t)-2*diff(y(t),t)+y(t) = 0; 
ic:=[y(0) = 4, D(y)(0) = 0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = -4 \,{\mathrm e}^{t} \left (-1+t \right ) \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 13

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

\begin{align*} y(t)&\to -4 e^t (t-1) \end{align*}

✓ Sympy. Time used: 0.087 (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): 4, Subs(Derivative(y(t), t), t, 0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (4 - 4 t\right ) e^{t} \]