78.5.13 problem 4 (b)

Internal problem ID [18085]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 9 (Integrating Factors). Problems at page 80
Problem number : 4 (b)
Date solved : Monday, March 31, 2025 at 05:07:32 PM
CAS classification : [_separable]

\begin{align*} y-x y^{\prime }&=x y^{3} y^{\prime } \end{align*}

✓ Maple. Time used: 0.042 (sec). Leaf size: 29

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

\[ y = \frac {x \,{\mathrm e}^{c_1}}{\left (\frac {x^{3} {\mathrm e}^{3 c_1}}{\operatorname {LambertW}\left (x^{3} {\mathrm e}^{3 c_1}\right )}\right )^{{1}/{3}}} \]

✓ Mathematica. Time used: 3.596 (sec). Leaf size: 76

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

\begin{align*} y(x)\to \sqrt [3]{W\left (e^{3 c_1} x^3\right )} \\ y(x)\to -\sqrt [3]{-1} \sqrt [3]{W\left (e^{3 c_1} x^3\right )} \\ y(x)\to (-1)^{2/3} \sqrt [3]{W\left (e^{3 c_1} x^3\right )} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.260 (sec). Leaf size: 15

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

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