29.20.12 problem 557

Internal problem ID [5153]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 557
Date solved : Sunday, March 30, 2025 at 06:45:37 AM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 72

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

\begin{align*} y &= \frac {-3 x^{2}+\sqrt {3}\, \sqrt {-x \left (x^{4}-3 x^{3}+4 c_1 \right )}}{6 x} \\ y &= \frac {-\sqrt {3}\, \sqrt {-x \left (x^{4}-3 x^{3}+4 c_1 \right )}-3 x^{2}}{6 x} \\ \end{align*}

✓ Mathematica. Time used: 0.529 (sec). Leaf size: 75

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

\begin{align*} y(x)\to -\frac {3 x^2+\sqrt {-3 x^5+9 x^4+36 c_1 x}}{6 x} \\ y(x)\to \frac {-3 x^2+\sqrt {-3 x^5+9 x^4+36 c_1 x}}{6 x} \\ \end{align*}

✗ Sympy

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

Timed Out