89.6.5 problem 5

Internal problem ID [24388]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Miscellaneous Exercises at page 45
Problem number : 5
Date solved : Thursday, October 02, 2025 at 10:23:35 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _dAlembert]

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 30

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

\[ y = \frac {\operatorname {RootOf}\left (x^{4} c_1^{4}+4 x c_1 \,\textit {\_Z}^{3}+k \,\textit {\_Z}^{4}-1\right )}{c_1} \]

✓ Mathematica. Time used: 60.149 (sec). Leaf size: 2229

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

Too large to display

✗ Sympy

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

Timed Out