60.1.189 problem 190

Internal problem ID [10203]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 190
Date solved : Monday, January 27, 2025 at 06:38:00 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

dsolve(sqrt(x^2-1)*diff(y(x),x) - sqrt(y(x)^2-1)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.317 (sec). Leaf size: 54

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

\begin{align*} y(x)\to \frac {1}{2} e^{-c_1} \left (\left (-1+e^{2 c_1}\right ) \sqrt {x^2-1}+\left (1+e^{2 c_1}\right ) x\right ) \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}