23.4.280 problem 283

Internal problem ID [6582]
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 : 283
Date solved : Friday, October 03, 2025 at 02:09:33 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} a y^{2}+x^{3} y^{\prime } y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 42

ode:=a*y(x)^2+x^3*diff(y(x),x)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ y &= {\mathrm e}^{\int _{}^{\ln \left (x \right )}\operatorname {RootOf}\left (-\int _{}^{\textit {\_Z}}\frac {\textit {\_a}}{\textit {\_a}^{3}-\textit {\_a}^{2}+a}d \textit {\_a} -\textit {\_b} +c_1 \right )d \textit {\_b} +c_2} \\ \end{align*}

✗ Mathematica

ode=a*y[x]^2 + x^3*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") 
a = symbols("a") 
y = Function("y") 
ode = Eq(a*y(x)**2 + x**3*Derivative(y(x), x)*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE a*y(x)**2/(x**3*Derivative(y(x), (x, 2))) + Derivative(y(x), x)