60.7.138 problem 1754 (book 6.163)

Internal problem ID [11688]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1754 (book 6.163)
Date solved : Sunday, March 30, 2025 at 08:42:33 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 12 y^{\prime \prime } y-15 {y^{\prime }}^{2}+8 y^{3}&=0 \end{align*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 151

ode:=12*diff(diff(y(x),x),x)*y(x)-15*diff(y(x),x)^2+8*y(x)^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ -\frac {12 y \left (8 \sqrt {y}-c_1 \right ) \sqrt {8 y-\sqrt {y}\, c_1}}{\sqrt {-24 y^{3}+3 c_1 y^{{5}/{2}}}\, c_1 \sqrt {\sqrt {y}\, \left (8 \sqrt {y}-c_1 \right )}}-x -c_2 &= 0 \\ \frac {12 y \left (8 \sqrt {y}-c_1 \right ) \sqrt {8 y-\sqrt {y}\, c_1}}{\sqrt {-24 y^{3}+3 c_1 y^{{5}/{2}}}\, c_1 \sqrt {\sqrt {y}\, \left (8 \sqrt {y}-c_1 \right )}}-x -c_2 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 0.695 (sec). Leaf size: 48

ode=8*y[x]^3 - 15*D[y[x],x]^2 + 12*y[x]*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {2304 c_1{}^2}{\left (3 c_1{}^2 x^2+6 c_2 c_1{}^2 x+128+3 c_2{}^2 c_1{}^2\right ){}^2} \\ y(x)\to 0 \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(8*y(x)**3 + 12*y(x)*Derivative(y(x), (x, 2)) - 15*Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -2*sqrt(15)*sqrt((2*y(x)**2 + 3*Derivative(y(x), (x, 2)))*y(x))/15 + Derivative(y(x), x) cannot be solved by the factorable group method