Internal problem ID [9326]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1748 (book 6.157).
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 {3 y^{\prime \prime } y-5 \left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 21
dsolve(3*diff(diff(y(x),x),x)*y(x)-5*diff(y(x),x)^2=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ -\frac {3}{2 y \relax (x )^{\frac {2}{3}}}-c_{1} x -c_{2} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.077 (sec). Leaf size: 20
DSolve[-5*y'[x]^2 + 3*y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2}{(2 x+3 c_1){}^{3/2}} \\ \end{align*}