Internal problem ID [4979]
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: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {2 x \sqrt {1-y^{2}}+y^{\prime } y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(2*x*sqrt(1-y(x)^2)+y(x)*diff(y(x),x)=0,y(x), singsol=all)
\[ c_{1}+x^{2}+\frac {\left (y \relax (x )-1\right ) \left (y \relax (x )+1\right )}{\sqrt {1-y \relax (x )^{2}}} = 0 \]
✓ Solution by Mathematica
Time used: 0.459 (sec). Leaf size: 67
DSolve[2*x*Sqrt[1-y[x]^2]+y[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {\left (x^2+1-c_1\right ) \left (-x^2+1+c_1\right )} \\ y(x)\to \sqrt {\left (x^2+1-c_1\right ) \left (-x^2+1+c_1\right )} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}