32.10.15 problem Exercise 35.15, page 504

Internal problem ID [6009]
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 35.15, page 504
Date solved : Monday, January 27, 2025 at 01:32:07 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 15

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

\[ y = -x +\left (c_1 +1\right ) \arctan \left (x \right )+c_2 \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 18

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

\[ y(x)\to (1+c_1) \arctan (x)-x+c_2 \]