40.2.11 problem 35

Internal problem ID [6589]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary problems. Page 22
Problem number : 35
Date solved : Monday, January 27, 2025 at 02:14:30 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 13

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

\[ y = \frac {c_1}{\sqrt {x^{2}+1}} \]

✓ Solution by Mathematica

Time used: 0.033 (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*}