Internal problem ID [12116]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\sqrt {-x^{2}+1}\, y^{\prime }-\sqrt {-y^{2}+1}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 9
dsolve(sqrt(1-x^2)*diff(y(x),x)-sqrt(1-y(x)^2)=0,y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (\arcsin \left (x \right )+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.488 (sec). Leaf size: 49
DSolve[Sqrt[1-x^2]*y'[x]-Sqrt[1-y[x]^2]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \cos \left (2 \arctan \left (\frac {\sqrt {1-x^2}}{x+1}\right )-c_1\right ) y(x)\to -1 y(x)\to 1 y(x)\to \text {Interval}[\{-1,1\}] \end{align*}