60.1.190 problem 191

Internal problem ID [10204]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 191
Date solved : Monday, January 27, 2025 at 06:38:09 PM
CAS classification : [_separable]

\begin{align*} \sqrt {-x^{2}+1}\, y^{\prime }-y \sqrt {y^{2}-1}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (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)
 

\[ \arcsin \left (x \right )+\arctan \left (\frac {1}{\sqrt {y^{2}-1}}\right )+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 1.112 (sec). Leaf size: 50

DSolve[Sqrt[1-x^2]*D[y[x],x] - y[x]*Sqrt[y[x]^2-1]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {\sec ^2(\arcsin (x)+c_1)} \\ y(x)\to \sqrt {\sec ^2(\arcsin (x)+c_1)} \\ y(x)\to -1 \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}