12.7.19 problem 20

Internal problem ID [1729]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page 91
Problem number : 20
Date solved : Saturday, March 29, 2025 at 11:37:41 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.033 (sec). Leaf size: 30

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

\[ y = {\mathrm e}^{-\frac {\operatorname {LambertW}\left ({\mathrm e}^{\frac {-2 c_1 x +2}{x}}\right ) x +2 c_1 x -2}{3 x}} \]

✓ Mathematica. Time used: 3.841 (sec). Leaf size: 82

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

✓ Sympy. Time used: 0.461 (sec). Leaf size: 17

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

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