67.2.43 problem Problem 18(h)

Internal problem ID [14000]
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 : Tuesday, January 28, 2025 at 06:11:23 AM
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*}

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[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,y[x],x,IncludeSingularSolutions -> True]
 

Not solved