32.10.14 problem Exercise 35.14, page 504

Internal problem ID [6008]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 8. Special second order equations. Lesson 35. Independent variable x absent
Problem number : Exercise 35.14, page 504
Date solved : Monday, January 27, 2025 at 01:32:06 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}+1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 33

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

\[ y = \frac {\ln \left (c_1 x -1\right ) c_1^{2}+c_2 \,c_1^{2}+c_1 x +\ln \left (c_1 x -1\right )}{c_1^{2}} \]

✓ Solution by Mathematica

Time used: 7.616 (sec). Leaf size: 33

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

\[ y(x)\to -x \cot (c_1)+\csc ^2(c_1) \log (-x \sin (c_1)-\cos (c_1))+c_2 \]