23.4.110 problem 110

Internal problem ID [6412]
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 : 110
Date solved : Tuesday, September 30, 2025 at 02:56:24 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} -6+x y \left (12+3 x y-2 x^{2} y^{2}\right )+x^{2} \left (9+2 x y\right ) y^{\prime }+2 x^{3} y^{\prime \prime }&=0 \end{align*}

✗ Maple

ode:=-6+x*y(x)*(12+3*x*y(x)-2*x^2*y(x)^2)+x^2*(9+2*x*y(x))*diff(y(x),x)+2*x^3*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=-6 + x*y[x]*(12 + 3*x*y[x] - 2*x^2*y[x]^2) + x^2*(9 + 2*x*y[x])*D[y[x],x] + 2*x^3*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**3*Derivative(y(x), (x, 2)) + x**2*(2*x*y(x) + 9)*Derivative(y(x), x) + x*(-2*x**2*y(x)**2 + 3*x*y(x) + 12)*y(x) - 6,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (2*x**3*y(x)**3 - 2*x**3*Derivative(y(x),