67.2.43 problem Problem 18(h)

Internal problem ID [13921]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 18(h)
Date solved : Wednesday, March 05, 2025 at 10:22:19 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \ln \left (x^{2}+1\right ) y^{\prime \prime }+\frac {4 x y^{\prime }}{x^{2}+1}+\frac {\left (-x^{2}+1\right ) y}{\left (x^{2}+1\right )^{2}}&=0 \end{align*}

✗ Maple

ode:=ln(x^2+1)*diff(diff(y(x),x),x)+4*x/(x^2+1)*diff(y(x),x)+(-x^2+1)/(x^2+1)^2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=Log[1+x^2]*D[y[x],{x,2}]+4*x/(1+x^2)*D[y[x],x]+(1-x^2)/(1+x^2)^2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x*Derivative(y(x), x)/(x**2 + 1) + (1 - x**2)*y(x)/(x**2 + 1)**2 + log(x**2 + 1)*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**4*log(x**2 + 1)*Derivative(y(x), (x, 2)) + x**2*y(x) - 2*x**2*log(x**2 + 1)*Derivative(y(x), (x, 2)) - y(x) - log(x**2 + 1)*Derivative(y(x), (x, 2)))/(4*x*(x**2 + 1)) cannot be solved by the factorable group method