Internal problem ID [951]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number: 25.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve(diff(y(x),x)*sqrt(1-x^2)+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: 0.317 (sec). Leaf size: 47
DSolve[y'[x]*Sqrt[1-x^2]+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*}