26.3.5 problem 4(b)

Internal problem ID [4265]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 10, page 47
Problem number : 4(b)
Date solved : Tuesday, March 04, 2025 at 06:02:55 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.015 (sec). Leaf size: 14

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

\[ y \left (x \right ) = \frac {1}{{\left (\frac {1}{\operatorname {LambertW}\left (c_{1} x^{3}\right )}\right )}^{{1}/{3}}} \]

✓ Mathematica. Time used: 3.684 (sec). Leaf size: 76

ode=y[x]-(x+x*y[x]^3)*D[y[x],x]==0; 
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: 0.277 (sec). Leaf size: 15

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

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