15.18.2 problem 2

Internal problem ID [3245]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 35, page 157
Problem number : 2
Date solved : Sunday, March 30, 2025 at 01:23:44 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 23

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

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

✓ Sympy. Time used: 0.075 (sec). Leaf size: 15

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

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