Internal problem ID [9332]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1753.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {12 y^{\prime \prime } y-15 \left (y^{\prime }\right )^{2}+8 y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.054 (sec). Leaf size: 151
dsolve(12*diff(diff(y(x),x),x)*y(x)-15*diff(y(x),x)^2+8*y(x)^3=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ -\frac {12 y \relax (x ) \left (8 \sqrt {y \relax (x )}-c_{1}\right ) \sqrt {8 y \relax (x )-\sqrt {y \relax (x )}\, c_{1}}}{\sqrt {-24 y \relax (x )^{3}+3 c_{1} y \relax (x )^{\frac {5}{2}}}\, c_{1} \sqrt {\sqrt {y \relax (x )}\, \left (8 \sqrt {y \relax (x )}-c_{1}\right )}}-x -c_{2} = 0 \\ \frac {12 y \relax (x ) \left (8 \sqrt {y \relax (x )}-c_{1}\right ) \sqrt {8 y \relax (x )-\sqrt {y \relax (x )}\, c_{1}}}{\sqrt {-24 y \relax (x )^{3}+3 c_{1} y \relax (x )^{\frac {5}{2}}}\, c_{1} \sqrt {\sqrt {y \relax (x )}\, \left (8 \sqrt {y \relax (x )}-c_{1}\right )}}-x -c_{2} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.359 (sec). Leaf size: 27
DSolve[8*y[x]^3 - 15*y'[x]^2 + 12*y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2304 c_1{}^2}{\left (128+3 c_1{}^2 (x+c_2){}^2\right ){}^2} \\ \end{align*}