54.3.349 problem 1366

Internal problem ID [12644]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1366
Date solved : Wednesday, October 01, 2025 at 02:18:52 AM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 2.088 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to \frac {c_2 x+c_1}{\sqrt {x^2+1}} \end{align*}

✗ Sympy

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

False