Internal problem ID [9333]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1754.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {n y y^{\prime \prime }-\left (-1+n \right ) \left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.039 (sec). Leaf size: 19
dsolve(n*y(x)*diff(diff(y(x),x),x)-(n-1)*diff(y(x),x)^2=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = \left (\frac {x c_{1}+c_{2}}{n}\right )^{n} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.1 (sec). Leaf size: 17
DSolve[(1 - n)*y'[x]^2 + n*y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 (x-c_1 n){}^n \\ \end{align*}