Internal problem ID [2318]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 37, page 171
Problem number: 5.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {\left (1-y^{2}\right ) {y^{\prime }}^{2}=1} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 48
dsolve((1-y(x)^2)*diff(y(x),x)^2=1,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \sin \left (\operatorname {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 \left (x \right ) = \sin \left (\operatorname {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: 0.089 (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 {$\#$1} \sqrt {1-\text {$\#$1}^2}-\arctan \left (\frac {\sqrt {1-\text {$\#$1}^2}}{\text {$\#$1}+1}\right )\&\right ][-x+c_1] y(x)\to \text {InverseFunction}\left [\frac {1}{2} \text {$\#$1} \sqrt {1-\text {$\#$1}^2}-\arctan \left (\frac {\sqrt {1-\text {$\#$1}^2}}{\text {$\#$1}+1}\right )\&\right ][x+c_1] \end{align*}