Internal problem ID [10778]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y-y^{\prime } x -\frac {1}{y}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(y(x)=x*diff(y(x),x)+1/y(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = \sqrt {c_{1} x^{2}+1} \\ y \left (x \right ) = -\sqrt {c_{1} x^{2}+1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.294 (sec). Leaf size: 53
DSolve[y[x]==x*y'[x]+1/y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {1+e^{2 c_1} x^2} \\ y(x)\to \sqrt {1+e^{2 c_1} x^2} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}