3.24 problem 24

Internal problem ID [7862]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 24
Date solved : Monday, October 21, 2024 at 04:30:21 PM
CAS classification : [NONE]

Solve

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

3.24.1 Maple step by step solution

3.24.2 Maple trace

Methods for second order ODEs:
 

3.24.3 Maple dsolve solution

Solving time : 0.191 (sec)
Leaf size : maple_leaf_size

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

\[ \text {No solution found} \]

3.24.4 Mathematica DSolve solution

Solving time : 0.0 (sec)
Leaf size : 0

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

Not solved