54.7.74 problem 1683 (book 6.92)

Internal problem ID [12923]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1683 (book 6.92)
Date solved : Wednesday, October 01, 2025 at 02:46:15 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Maple

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

\[ \text {No solution found} \]

✓ Mathematica. Time used: 45.021 (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) + 12/x**2 + 24/(x**3*y(x)) cannot be solved by the factorable group method