88.6.6 problem 6

Internal problem ID [23988]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 38
Problem number : 6
Date solved : Thursday, October 02, 2025 at 09:49:26 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 58

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

\begin{align*} y &= \left (3 \ln \left (x \right )+c_1 \right )^{{1}/{3}} x \\ y &= -\frac {\left (3 \ln \left (x \right )+c_1 \right )^{{1}/{3}} \left (1+i \sqrt {3}\right ) x}{2} \\ y &= \frac {\left (3 \ln \left (x \right )+c_1 \right )^{{1}/{3}} \left (i \sqrt {3}-1\right ) x}{2} \\ \end{align*}

✓ Mathematica. Time used: 0.116 (sec). Leaf size: 63

ode=D[y[x],{x,1}]==(x^3+y[x]^3)/(x*y[x]^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.936 (sec). Leaf size: 68

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

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