Internal problem ID [10158]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 19. Summary.
Page 29
Problem number: Ex 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\sqrt {1-y^{2}}+\sqrt {-x^{2}+1}\, y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 11
dsolve(sqrt(1-y(x)^2)+sqrt(1-x^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\sin \left (\arcsin \relax (x )+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.279 (sec). Leaf size: 31
DSolve[Sqrt[1-y[x]^2]+Sqrt[1-x^2]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\cos (\text {ArcCos}(x)+c_1) \\ y(x)\to -1 \\ y(x)\to 1 \\ y(x)\to \text {Interval}[\{-1,1\}] \\ \end{align*}