60.1.60 problem 60

Internal problem ID [10074]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 60
Date solved : Monday, January 27, 2025 at 06:21:57 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 29

dsolve(diff(y(x),x) - sqrt(y(x)^2-1)/sqrt(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: 0.320 (sec). Leaf size: 54

DSolve[D[y[x],x] - Sqrt[y[x]^2-1]/Sqrt[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*}