30.4.14 problem 15

Internal problem ID [7497]
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 : 15
Date solved : Tuesday, September 30, 2025 at 04:39:46 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 2.446 (sec). Leaf size: 35

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

\begin{align*} y(x)&\to \frac {W\left (\frac {e^{-1+\frac {9 c_1}{2^{2/3}}}}{x^2}\right )}{2 x}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.367 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = \frac {W\left (\frac {C_{1}}{x^{2}}\right )}{2 x} \]