68.2.4 problem Problem 3.7(d)

Internal problem ID [14070]
Book : Differential Equations, Linear, Nonlinear, Ordinary, Partial. A.C. King, J.Billingham, S.R.Otto. Cambridge Univ. Press 2003
Section : Chapter 3 Bessel functions. Problems page 89
Problem number : Problem 3.7(d)
Date solved : Wednesday, March 05, 2025 at 10:28:09 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 17

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

\[ y = c_{1} \sin \left (\alpha x \right )+c_{2} \cos \left (\alpha x \right ) \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 20

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

\[ y(x)\to c_1 \cos (a x)+c_2 \sin (a x) \]

✓ Sympy. Time used: 0.094 (sec). Leaf size: 19

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

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