Internal problem ID [934]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } \left (x^{2}+1\right )+y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 13
dsolve(diff(y(x),x)*(1+x^2)+x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{\sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 22
DSolve[y'[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*}