23.4.196 problem 196

Internal problem ID [6498]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 4. THE NONLINEAR EQUATION OF SECOND ORDER, page 380
Problem number : 196
Date solved : Tuesday, September 30, 2025 at 03:02:21 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 151

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

\begin{align*} y &= 0 \\ -\frac {12 y \left (8 \sqrt {y}-c_1 \right ) \sqrt {8 y-c_1 \sqrt {y}}}{\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-c_1 \sqrt {y}}}{\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: 0.398 (sec). Leaf size: 48

ode=12*y[x]*D[y[x],{x,2}] == -8*y[x]^3 + 15*D[y[x],x]^2; 
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))/