56.3.24 problem 24

Internal problem ID [8882]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 24
Date solved : Sunday, March 30, 2025 at 01:52:13 PM
CAS classification : [NONE]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

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