86.6.7 problem 7

Internal problem ID [23140]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 5. Linear equations of the second order with constant coefficients. Exercise 5b at page 77
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:23:25 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} z^{\prime \prime }-7 z^{\prime }-13 z&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 24

ode:=diff(diff(z(t),t),t)-7*diff(z(t),t)-13*z(t) = 0; 
dsolve(ode,z(t), singsol=all);
 

\[ z = \left (c_1 \,{\mathrm e}^{t \sqrt {101}}+c_2 \right ) {\mathrm e}^{-\frac {\left (-7+\sqrt {101}\right ) t}{2}} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 35

ode=D[z[t],{t,2}]-7*D[z[t],t]-13*z[t]==0; 
ic={}; 
DSolve[{ode,ic},z[t],t,IncludeSingularSolutions->True]
 

\begin{align*} z(t)&\to e^{-\frac {1}{2} \left (\sqrt {101}-7\right ) t} \left (c_2 e^{\sqrt {101} t}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.109 (sec). Leaf size: 29

from sympy import * 
t = symbols("t") 
z = Function("z") 
ode = Eq(-13*z(t) - 7*Derivative(z(t), t) + Derivative(z(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=z(t),ics=ics)
 

\[ z{\left (t \right )} = C_{1} e^{\frac {t \left (7 - \sqrt {101}\right )}{2}} + C_{2} e^{\frac {t \left (7 + \sqrt {101}\right )}{2}} \]