81.10.8 problem 14-8

Internal problem ID [21603]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 14. Second order homogeneous differential equations with constant coefficients. Page 297.
Problem number : 14-8
Date solved : Thursday, October 02, 2025 at 07:58:55 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

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

\[ y = \left (c_1 \,{\mathrm e}^{2 x \sqrt {2}}+c_2 \right ) {\mathrm e}^{-\left (\sqrt {2}-1\right ) x} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 34

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

\begin{align*} y(x)&\to e^{x-\sqrt {2} x} \left (c_2 e^{2 \sqrt {2} x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.118 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) - 22*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{x \left (11 - \sqrt {122}\right )} + C_{2} e^{x \left (11 + \sqrt {122}\right )} \]