56.3.25 problem 25

Internal problem ID [8883]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 25
Date solved : Monday, January 27, 2025 at 05:18:27 PM
CAS classification : [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 14

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

\[ y = \int \frac {1}{\arctan \left (x \right )+c_{1}}d x +c_{2} \]

✓ Solution by Mathematica

Time used: 60.287 (sec). Leaf size: 25

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

\[ y(x)\to \int _1^x\frac {1}{\arctan (K[1])-c_1}dK[1]+c_2 \]