32.4.4 problem Recognizable Exact Differential equations. Integrating factors. Example 10.701, page 90

Internal problem ID [5815]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 10
Problem number : Recognizable Exact Differential equations. Integrating factors. Example 10.701, page 90
Date solved : Monday, January 27, 2025 at 01:19:55 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

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

\[ y \left (x \right ) = \frac {c_{1}}{\sqrt {x^{2}+1}} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 22

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

\begin{align*} y(x)\to \frac {c_1}{\sqrt {x^2+1}} \\ y(x)\to 0 \\ \end{align*}