23.4.108 problem 108

Internal problem ID [6410]
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 : 108
Date solved : Tuesday, September 30, 2025 at 02:56:23 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 24+12 x y+x^{3} \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right )&=0 \end{align*}

✗ Maple

ode:=24+12*x*y(x)+x^3*(-y(x)^3+y(x)*diff(y(x),x)+diff(diff(y(x),x),x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 44.232 (sec). Leaf size: 40

ode=24 + 12*x*y[x] + x^3*(-y[x]^3 + y[x]*D[y[x],x] + D[y[x],{x,2}]) == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {2+x^3 \wp '(x+c_1;0,c_2)}{x-x^3 \wp (x+c_1;0,c_2)} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*(-y(x)**3 + y(x)*Derivative(y(x), x) + Derivative(y(x), (x, 2))) + 12*x*y(x) + 24,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -y(x)**2 + Derivative(y(x), x) + Derivative(y(x), (x, 2))/y(x) +