Internal problem ID [3706]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 33
Problem number: 981.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (1-y^{2}\right ) \left (y^{\prime }\right )^{2}-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.25 (sec). Leaf size: 48
dsolve((1-y(x)^2)*diff(y(x),x)^2 = 1,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sin \left (\RootOf \left (\sin \left (\textit {\_Z} \right ) \sqrt {\frac {\cos \left (2 \textit {\_Z} \right )}{2}+\frac {1}{2}}+\textit {\_Z} +2 c_{1}-2 x \right )\right ) \\ y \relax (x ) = \sin \left (\RootOf \left (-\sin \left (\textit {\_Z} \right ) \sqrt {\frac {\cos \left (2 \textit {\_Z} \right )}{2}+\frac {1}{2}}-\textit {\_Z} +2 c_{1}-2 x \right )\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.09 (sec). Leaf size: 105
DSolve[(1-y[x]^2) (y'[x])^2==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {1}{2} \text {$\#$1} \sqrt {1-\text {$\#$1}^2}-\text {ArcTan}\left (\frac {\sqrt {1-\text {$\#$1}^2}}{\text {$\#$1}+1}\right )\&\right ][-x+c_1] \\ y(x)\to \text {InverseFunction}\left [\frac {1}{2} \text {$\#$1} \sqrt {1-\text {$\#$1}^2}-\text {ArcTan}\left (\frac {\sqrt {1-\text {$\#$1}^2}}{\text {$\#$1}+1}\right )\&\right ][x+c_1] \\ \end{align*}