81.10.2 problem 14-2

Internal problem ID [21597]
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 : 14-2
Date solved : Thursday, October 02, 2025 at 07:58:51 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-5 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 22

ode:=diff(diff(y(x),x),x)-5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{\sqrt {5}\, x}+c_2 \,{\mathrm e}^{-\sqrt {5}\, x} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 31

ode=D[y[x],{x,2}]-5*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{\sqrt {5} x}+c_2 e^{-\sqrt {5} x} \end{align*}

✓ Sympy. Time used: 0.042 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-5*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- \sqrt {5} x} + C_{2} e^{\sqrt {5} x} \]