Internal problem ID [8397]
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]
\[ \boxed {y^{\prime }-\frac {\sqrt {y^{2}-1}}{\sqrt {x^{2}-1}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x) - sqrt(y(x)^2-1)/sqrt(x^2-1)=0,y(x), singsol=all)
\[ \ln \left (x +\sqrt {x^{2}-1}\right )-\ln \left (y \left (x \right )+\sqrt {y \left (x \right )^{2}-1}\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 4.959 (sec). Leaf size: 153
DSolve[y'[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} \sqrt {2 x^2-2 \sqrt {x^2-1} x+e^{4 c_1} \left (2 x^2+2 \sqrt {x^2-1} x-1\right )-1+2 e^{2 c_1}} \\ y(x)\to \frac {1}{2} e^{-c_1} \sqrt {2 x^2-2 \sqrt {x^2-1} x+e^{4 c_1} \left (2 x^2+2 \sqrt {x^2-1} x-1\right )-1+2 e^{2 c_1}} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}