60.1.334 problem 335

Internal problem ID [10348]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 335
Date solved : Monday, January 27, 2025 at 07:18:30 PM
CAS classification : [_separable]

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

✓ Solution by Maple

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

dsolve((y(x)^2-1)^(1/2)*diff(y(x),x)-(x^2-1)^(1/2) = 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: 0.640 (sec). Leaf size: 75

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

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