Internal problem ID [11214]
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]
\[ \boxed {\left (x^{2}+1\right ) {y^{\prime }}^{2}=1} \]
✓ Solution by Maple
Time used: 0.36 (sec). Leaf size: 17
dsolve((1+x^2)*diff(y(x),x)^2=1,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \operatorname {arcsinh}\left (x \right )+c_{1} y \left (x \right ) = -\operatorname {arcsinh}\left (x \right )+c_{1} \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 45
DSolve[(1+x^2)*(y'[x])^2==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\log \left (\sqrt {x^2+1}-x\right )+c_1 y(x)\to \log \left (\sqrt {x^2+1}-x\right )+c_1 \end{align*}