Internal problem ID [2715]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 82.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {x \left (\left (y^{\prime }\right )^{2}-1\right )-2 y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 49
dsolve(x*( (diff(y(x),x))^2-1)=2*diff(y(x),x) ,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {x^{2}+1}-\arctanh \left (\frac {1}{\sqrt {x^{2}+1}}\right )+\ln \relax (x )+c_{1} \\ y \relax (x ) = -\sqrt {x^{2}+1}+\arctanh \left (\frac {1}{\sqrt {x^{2}+1}}\right )+\ln \relax (x )+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 59
DSolve[x*( (y'[x])^2-1)==2*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {x^2+1}+\log \left (\sqrt {x^2+1}-1\right )+c_1 \\ y(x)\to -\sqrt {x^2+1}+\log \left (\sqrt {x^2+1}+1\right )+c_1 \\ \end{align*}