59.3.9 problem David Saunders 1981 paper. Example 3

Internal problem ID [10011]
Book : Collection of Kovacic problems
Section : section 3. Problems from Kovacic related papers
Problem number : David Saunders 1981 paper. Example 3
Date solved : Wednesday, March 05, 2025 at 08:04:10 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

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

\[ y = \frac {c_{2} x^{3}+c_{1}}{x} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 18

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

\[ y(x)\to \frac {c_2 x^3+c_1}{x} \]

✓ Sympy. Time used: 0.057 (sec). Leaf size: 10

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

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