Internal problem ID [4978]
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: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\frac {1}{\sqrt {-x^{2}+1}}+\frac {y^{\prime }}{\sqrt {1-y^{2}}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 11
dsolve(1/sqrt(1-x^2)+diff(y(x),x)/sqrt(1-y(x)^2)=0,y(x), singsol=all)
\[ y \relax (x ) = -\sin \left (\arcsin \relax (x )+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 2.778 (sec). Leaf size: 104
DSolve[1/Sqrt[1-x^2]+y'[x]/Sqrt[1-y[x]^2]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\tan \left (\text {ArcTan}\left (\frac {x}{\sqrt {1-x^2}}\right )-c_1\right )}{\sqrt {\sec ^2\left (\text {ArcTan}\left (\frac {x}{\sqrt {1-x^2}}\right )-c_1\right )}} \\ y(x)\to \frac {\tan \left (\text {ArcTan}\left (\frac {x}{\sqrt {1-x^2}}\right )-c_1\right )}{\sqrt {\sec ^2\left (\text {ArcTan}\left (\frac {x}{\sqrt {1-x^2}}\right )-c_1\right )}} \\ \end{align*}