Internal problem ID [8042]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 462.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y \left (y^{\prime }\right )^{2}-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 27
dsolve(y(x)*diff(y(x),x)^2-1 = 0,y(x), singsol=all)
\begin{align*} x -\frac {2 y \relax (x )^{\frac {3}{2}}}{3}-c_{1} = 0 \\ x +\frac {2 y \relax (x )^{\frac {3}{2}}}{3}-c_{1} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 43
DSolve[-1 + y[x]*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (\frac {3}{2}\right )^{2/3} (-x+c_1){}^{2/3} \\ y(x)\to \left (\frac {3}{2}\right )^{2/3} (x+c_1){}^{2/3} \\ \end{align*}