Internal problem ID [7771]
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]
Solve \begin {gather*} \boxed {\sqrt {-x^{2}+1}\, y^{\prime }-y \sqrt {y^{2}-1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (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)
\[ \arcsin \relax (x )+\arctan \left (\frac {1}{\sqrt {-1+y \relax (x )^{2}}}\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 1.756 (sec). Leaf size: 74
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 {\sec ^2\left (\operatorname {ArcTan}\left (\frac {x}{\sqrt {1-x^2}}\right )+c_1\right )} \\ y(x)\to \sqrt {\sec ^2\left (\operatorname {ArcTan}\left (\frac {x}{\sqrt {1-x^2}}\right )+c_1\right )} \\ y(x)\to -1 \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}