60.3.295 problem 1312

Internal problem ID [11291]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1312
Date solved : Sunday, March 30, 2025 at 08:08:11 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} x \left (x^{2}+1\right ) y^{\prime \prime }+2 \left (x^{2}-1\right ) y^{\prime }-2 x y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

ode:=x*(x^2+1)*diff(diff(y(x),x),x)+2*(x^2-1)*diff(y(x),x)-2*x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2 \,x^{3}+c_1}{x^{2}+1} \]

✓ Mathematica. Time used: 0.207 (sec). Leaf size: 53

ode=-2*x*y[x] + 2*(-1 + x^2)*D[y[x],x] + x*(1 + x^2)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\left (c_2 x^3+3 c_1\right ) \exp \left (-\frac {1}{2} \int _1^x\frac {2 \left (K[1]^2-1\right )}{K[1]^3+K[1]}dK[1]\right )}{3 x} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(x**2 + 1)*Derivative(y(x), (x, 2)) - 2*x*y(x) + (2*x**2 - 2)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False