Internal problem ID [7642]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 61.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\sqrt {x^{2}-1}}{\sqrt {y^{2}-1}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 50
dsolve(diff(y(x),x) - sqrt(x^2-1)/sqrt(y(x)^2-1)=0,y(x), singsol=all)
\[ c_{1}+\sqrt {x^{2}-1}\, x -\ln \left (x +\sqrt {x^{2}-1}\right )-y \relax (x ) \sqrt {-1+y \relax (x )^{2}}+\ln \left (y \relax (x )+\sqrt {-1+y \relax (x )^{2}}\right ) = 0 \]
✓ Solution by Mathematica
Time used: 0.976 (sec). Leaf size: 77
DSolve[y'[x] - Sqrt[x^2-1]/Sqrt[y[x]^2-1]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {1}{2} \text {$\#$1} \sqrt {\text {$\#$1}^2-1}-\tanh ^{-1}\left (\frac {\sqrt {\text {$\#$1}^2-1}}{\text {$\#$1}-1}\right )\&\right ]\left [\frac {1}{2} \sqrt {x^2-1} x+\coth ^{-1}\left (\frac {1-x}{\sqrt {x^2-1}}\right )+c_1\right ] \\ \end{align*}