68.2.3 problem Problem 3.7(c)

Internal problem ID [14077]
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(c)
Date solved : Monday, March 31, 2025 at 12:02:47 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

\[ y = c_1 \operatorname {AiryAi}\left (-x \right )+c_2 \operatorname {AiryBi}\left (-x \right ) \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 28

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

\[ y(x)\to c_1 \operatorname {AiryAi}\left (\sqrt [3]{-1} x\right )+c_2 \operatorname {AiryBi}\left (\sqrt [3]{-1} x\right ) \]

✓ Sympy. Time used: 0.086 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = C_{1} Ai\left (- x\right ) + C_{2} Bi\left (- x\right ) \]