Internal problem ID [4970]
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: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {2 x^{2} y y^{\prime }+y^{2}-2=0} \end {gather*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 29
dsolve(2*x^2*y(x)*diff(y(x),x)+y(x)^2=2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {{\mathrm e}^{\frac {1}{x}} c_{1}+2} \\ y \relax (x ) = -\sqrt {{\mathrm e}^{\frac {1}{x}} c_{1}+2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.281 (sec). Leaf size: 70
DSolve[2*x*y[x]*y'[x]+y[x]^2==2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {2 x+e^{2 c_1}}}{\sqrt {x}} \\ y(x)\to \frac {\sqrt {2 x+e^{2 c_1}}}{\sqrt {x}} \\ y(x)\to -\sqrt {2} \\ y(x)\to \sqrt {2} \\ \end{align*}