Internal problem ID [1886]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 5, page 21
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y x +\sqrt {x^{2}+1}\, y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(x*y(x)+sqrt(1+x^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-\sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 26
DSolve[x*y[x]+Sqrt[1+x^2]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-\sqrt {x^2+1}} \\ y(x)\to 0 \\ \end{align*}