Internal problem ID [4966]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page
7
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x y y^{\prime }-\sqrt {1+y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x*y(x)*diff(y(x),x)=sqrt(1+y(x)^2),y(x), singsol=all)
\[ \ln \relax (x )-\sqrt {1+y \relax (x )^{2}}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.356 (sec). Leaf size: 59
DSolve[x*y[x]*y'[x]==Sqrt[1+y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {(\log (x)-1+c_1) (\log (x)+1+c_1)} \\ y(x)\to \sqrt {(\log (x)-1+c_1) (\log (x)+1+c_1)} \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}