Internal problem ID [5719]
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]
\[ \boxed {x y y^{\prime }-\sqrt {y^{2}+1}=0} \]
✓ 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)
\[ \ln \left (x \right )-\sqrt {1+y \left (x \right )^{2}}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.229 (sec). Leaf size: 65
DSolve[x*y[x]*y'[x]==Sqrt[1+y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {\log ^2(x)+2 c_1 \log (x)-1+c_1{}^2} y(x)\to \sqrt {\log ^2(x)+2 c_1 \log (x)-1+c_1{}^2} y(x)\to -i y(x)\to i \end{align*}