88.10.11 problem 11

Internal problem ID [24046]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 52
Problem number : 11
Date solved : Thursday, October 02, 2025 at 09:55:10 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 23

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

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

✓ Sympy. Time used: 0.044 (sec). Leaf size: 15

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

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