29.24.26 problem 688

Internal problem ID [5279]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 24
Problem number : 688
Date solved : Tuesday, March 04, 2025 at 09:04:39 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _dAlembert]

\begin{align*} \left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3}&=0 \end{align*}

✓ Maple. Time used: 0.066 (sec). Leaf size: 50

ode:=(3*x^3+6*x^2*y(x)-3*x*y(x)^2+20*y(x)^3)*diff(y(x),x)+4*x^3+9*x^2*y(x)+6*x*y(x)^2-y(x)^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (c_{1}^{4} x^{4}+3 \textit {\_Z} \,c_{1}^{3} x^{3}+3 \textit {\_Z}^{2} c_{1}^{2} x^{2}-\textit {\_Z}^{3} c_{1} x +5 \textit {\_Z}^{4}-1\right )}{c_{1}} \]

✓ Mathematica. Time used: 60.182 (sec). Leaf size: 2201

ode=(3 x^3+6 x^2 y[x]-3 x y[x]^2+20 y[x]^3)D[y[x],x]+4 x^3+9 x^2 y[x]+6 x y[x]^2-y[x]^3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**3 + 9*x**2*y(x) + 6*x*y(x)**2 + (3*x**3 + 6*x**2*y(x) - 3*x*y(x)**2 + 20*y(x)**3)*Derivative(y(x), x) - y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out