23.2.302 problem 322

Internal problem ID [5657]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 322
Date solved : Tuesday, September 30, 2025 at 01:24:14 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} x {y^{\prime }}^{3}-3 x^{2} y {y^{\prime }}^{2}+x \left (x^{5}+3 y^{2}\right ) y^{\prime }-2 x^{5} y-y^{3}&=0 \end{align*}

✗ Maple

ode:=x*diff(y(x),x)^3-3*x^2*y(x)*diff(y(x),x)^2+x*(x^5+3*y(x)^2)*diff(y(x),x)-2*x^5*y(x)-y(x)^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=x (D[y[x],x])^3 -3 x^2 y[x] (D[y[x],x])^2 +x(x^5+3 y[x]^2) D[y[x],x]-2 x^5 y[x]- y[x]^3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x**5*y(x) - 3*x**2*y(x)*Derivative(y(x), x)**2 + x*(x**5 + 3*y(x)**2)*Derivative(y(x), x) + x*Derivative(y(x), x)**3 - y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out