12.3.7 problem 8

Internal problem ID [1584]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number : 8
Date solved : Monday, January 27, 2025 at 05:09:25 AM
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(diff(y(x),x)*(1+x^2)+x*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 22

DSolve[D[y[x],x]*(1+x^2)+x*y[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*}