73.7.10 problem 10

Internal problem ID [15089]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 10
Date solved : Thursday, March 13, 2025 at 05:37:15 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 72

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

\begin{align*} y &= \frac {\left (-4 x^{6}+8 c_{1} \right )^{{1}/{3}}}{2 x} \\ y &= -\frac {\left (-4 x^{6}+8 c_{1} \right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{4 x} \\ y &= \frac {\left (-4 x^{6}+8 c_{1} \right )^{{1}/{3}} \left (i \sqrt {3}-1\right )}{4 x} \\ \end{align*}

✓ Mathematica. Time used: 0.23 (sec). Leaf size: 80

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

\begin{align*} y(x)\to -\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{-x^6+2 c_1}}{x} \\ y(x)\to \frac {\sqrt [3]{-\frac {x^6}{2}+c_1}}{x} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{-\frac {x^6}{2}+c_1}}{x} \\ \end{align*}

✓ Sympy. Time used: 1.483 (sec). Leaf size: 80

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

\[ \left [ y{\left (x \right )} = \frac {2^{\frac {2}{3}} \sqrt [3]{\frac {C_{1}}{x^{3}} - x^{3}}}{2}, \ y{\left (x \right )} = \frac {2^{\frac {2}{3}} \left (-1 - \sqrt {3} i\right ) \sqrt [3]{\frac {C_{1}}{x^{3}} - x^{3}}}{4}, \ y{\left (x \right )} = \frac {2^{\frac {2}{3}} \left (-1 + \sqrt {3} i\right ) \sqrt [3]{\frac {C_{1}}{x^{3}} - x^{3}}}{4}\right ] \]