Internal problem ID [7641]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 60.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\sqrt {y^{2}-1}}{\sqrt {x^{2}-1}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve(diff(y(x),x) - sqrt(y(x)^2-1)/sqrt(x^2-1)=0,y(x), singsol=all)
\[ \ln \left (x +\sqrt {x^{2}-1}\right )-\ln \left (y \relax (x )+\sqrt {-1+y \relax (x )^{2}}\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 5.34 (sec). Leaf size: 130
DSolve[y'[x] - Sqrt[y[x]^2-1]/Sqrt[x^2-1]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^{-c_1} \sqrt {e^{2 c_1} \left (\left (2 x^2-1\right ) \cosh (2 c_1)+2 x \sqrt {x^2-1} \sinh (2 c_1)+1\right )}}{\sqrt {2}} \\ y(x)\to \frac {e^{-c_1} \sqrt {e^{2 c_1} \left (\left (2 x^2-1\right ) \cosh (2 c_1)+2 x \sqrt {x^2-1} \sinh (2 c_1)+1\right )}}{\sqrt {2}} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}