Internal problem ID [7770]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 191.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\sqrt {1-x^{2}}\, y^{\prime }-y \sqrt {y^{2}-1}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(sqrt(1-x^2)*diff(y(x),x) - y(x)*sqrt(y(x)^2-1)=0,y(x), singsol=all)
\[ \arcsin \left (x \right )+\arctan \left (\frac {1}{\sqrt {y \left (x \right )^{2}-1}}\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 2.035 (sec). Leaf size: 80
DSolve[Sqrt[1-x^2]*y'[x] - y[x]*Sqrt[y[x]^2-1]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {\frac {1}{\left (\sqrt {1-x^2} \sin (c_1)+x \cos (c_1)\right ){}^2}} \\ y(x)\to \sqrt {\frac {1}{\left (\sqrt {1-x^2} \sin (c_1)+x \cos (c_1)\right ){}^2}} \\ y(x)\to -1 \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}