23.4.115 problem 115

Internal problem ID [6417]
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 : 115
Date solved : Tuesday, September 30, 2025 at 02:56:26 PM
CAS classification : [NONE]

\begin{align*} 24-48 x y+\left (-12 x^{2}+1\right ) \left (y^{2}+3 y^{\prime }\right )+2 x \left (-4 x^{2}+1\right ) \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right )&=0 \end{align*}

✗ Maple

ode:=24-48*x*y(x)+(-12*x^2+1)*(y(x)^2+3*diff(y(x),x))+2*x*(-4*x^2+1)*(-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

ode=24 - 48*x*y[x] + (1 - 12*x^2)*(y[x]^2 + 3*D[y[x],x]) + 2*x*(1 - 4*x^2)*(-y[x]^3 + y[x]*D[y[x],x] + D[y[x],{x,2}]) == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*(1 - 4*x**2)*(-y(x)**3 + y(x)*Derivative(y(x), x) + Derivative(y(x), (x, 2))) - 48*x*y(x) + (1 - 12*x**2)*(y(x)**2 + 3*Derivative(y(x), x)) + 24,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (8*x**3*y(x)**3 - 8*x**3*Derivative(y(x),