78.7.3 problem 1 (c)

Internal problem ID [18118]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 11 (Reduction of order). Problems at page 87
Problem number : 1 (c)
Date solved : Monday, March 31, 2025 at 05:12:12 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 22

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

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 31

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

\[ y(x)\to c_1 e^{\sqrt {k} x}+c_2 e^{-\sqrt {k} x} \]

✓ Sympy. Time used: 0.074 (sec). Leaf size: 22

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

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