30.12.8 problem 8

Internal problem ID [7600]
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 : 8
Date solved : Tuesday, September 30, 2025 at 04:54:48 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 24

ode:=diff(diff(z(t),t),t)+diff(z(t),t)-z(t) = 0; 
dsolve(ode,z(t), singsol=all);
 

\[ z = \left (c_1 \,{\mathrm e}^{t \sqrt {5}}+c_2 \right ) {\mathrm e}^{-\frac {\left (\sqrt {5}+1\right ) t}{2}} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 35

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

\begin{align*} z(t)&\to e^{-\frac {1}{2} \left (1+\sqrt {5}\right ) t} \left (c_2 e^{\sqrt {5} t}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.096 (sec). Leaf size: 29

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

\[ z{\left (t \right )} = C_{1} e^{\frac {t \left (-1 + \sqrt {5}\right )}{2}} + C_{2} e^{- \frac {t \left (1 + \sqrt {5}\right )}{2}} \]