Internal problem ID [5732]
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]
\[ \boxed {2 x \sqrt {1-y^{2}}+y y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(2*x*sqrt(1-y(x)^2)+y(x)*diff(y(x),x)=0,y(x), singsol=all)
\[ c_{1} +x^{2}+\frac {\left (y \left (x \right )-1\right ) \left (y \left (x \right )+1\right )}{\sqrt {1-y \left (x \right )^{2}}} = 0 \]
✓ Solution by Mathematica
Time used: 0.288 (sec). Leaf size: 69
DSolve[2*x*Sqrt[1-y[x]^2]+y[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-x^4+2 c_1 x^2+1-c_1{}^2} y(x)\to \sqrt {-x^4+2 c_1 x^2+1-c_1{}^2} y(x)\to -1 y(x)\to 1 \end{align*}