30.4.12 problem 12

Internal problem ID [7495]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.5, Special Integrating Factors. Exercises. page 69
Problem number : 12
Date solved : Tuesday, September 30, 2025 at 04:39:40 PM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} 2 x y^{3}+1+\left (3 x^{2} y^{2}-\frac {1}{y}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 44

ode:=2*x*y(x)^3+1+(3*x^2*y(x)^2-1/y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{c_1 +x} 3^{{2}/{3}}}{3 \left (-\frac {x^{2} {\mathrm e}^{3 c_1 +3 x}}{\operatorname {LambertW}\left (-3 x^{2} {\mathrm e}^{3 c_1 +3 x}\right )}\right )^{{1}/{3}}} \]

✓ Mathematica. Time used: 2.815 (sec). Leaf size: 120

ode=( 2*x*y[x]^3+1 )+( 3*x^2*y[x]^2 -1/y[x])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*y(x)**3 + (3*x**2*y(x)**2 - 1/y(x))*Derivative(y(x), x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out