30.12.4 problem 4

Internal problem ID [7596]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 4, Linear Second-Order Equations. EXERCISES 4.2 at page 164
Problem number : 4
Date solved : Tuesday, September 30, 2025 at 04:54:46 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=diff(diff(y(t),t),t)-diff(y(t),t)-2*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{2 t}+c_2 \,{\mathrm e}^{-t} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 22

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

\begin{align*} y(t)&\to e^{-t} \left (c_2 e^{3 t}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.090 (sec). Leaf size: 14

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

\[ y{\left (t \right )} = C_{1} e^{- t} + C_{2} e^{2 t} \]