60.1.61 problem 61

Internal problem ID [10075]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 61
Date solved : Monday, January 27, 2025 at 06:22:12 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 50

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

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

✓ Solution by Mathematica

Time used: 0.688 (sec). Leaf size: 75

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

\[ y(x)\to \text {InverseFunction}\left [\frac {1}{2} \text {$\#$1} \sqrt {\text {$\#$1}^2-1}-\frac {1}{2} \log \left (\sqrt {\text {$\#$1}^2-1}+\text {$\#$1}\right )\&\right ]\left [-\frac {1}{2} \text {arctanh}\left (\frac {x}{\sqrt {x^2-1}}\right )+\frac {1}{2} \sqrt {x^2-1} x+c_1\right ] \]