Internal problem ID [4176]
Book: A treatise on ordinary and partial differential equations by William Woolsey Johnson.
1913
Section: Chapter 1, Nature and meaning of a differential equation between two variables. page
12
Problem number: 4.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2} \left (-x^{2}+1\right )+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.12 (sec). Leaf size: 33
dsolve(diff(y(x),x)^2*(1-x^2)+1=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \ln \left (x +\sqrt {x^{2}-1}\right )+c_{1} \\ y \relax (x ) = -\ln \left (x +\sqrt {x^{2}-1}\right )+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 41
DSolve[y'[x]^2*(1-x^2)+1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\tanh ^{-1}\left (\frac {x}{\sqrt {x^2-1}}\right )+c_1 \\ y(x)\to \tanh ^{-1}\left (\frac {x}{\sqrt {x^2-1}}\right )+c_1 \\ \end{align*}