59.1.820 problem 844

Internal problem ID [9992]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 844
Date solved : Sunday, March 30, 2025 at 02:51:07 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

\[ y = \frac {c_2 \,x^{3}+c_1}{x} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 18

ode=D[y[x],{x,2}]==((4*(3/2)^2-1)/(4*x^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: 0.068 (sec). Leaf size: 10

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

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