Internal problem ID [10190]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IV, differential equations of the first order and higher degree than the first. Article
24. Equations solvable for \(p\). Page 49
Problem number: Ex 5.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) \left (y^{\prime }\right )^{2}-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve((1+x^2)*diff(y(x),x)^2=1,y(x), singsol=all)
\begin{align*} y \relax (x ) = \arcsinh \relax (x )+c_{1} \\ y \relax (x ) = -\arcsinh \relax (x )+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 21
DSolve[(1+x^2)*(y'[x])^2==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sinh ^{-1}(x)+c_1 \\ y(x)\to -\sinh ^{-1}(x)+c_1 \\ \end{align*}