30.4.15 problem 16

Internal problem ID [7498]
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 : 16
Date solved : Tuesday, September 30, 2025 at 04:39:49 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 37

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

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

✓ Mathematica. Time used: 9.6 (sec). Leaf size: 420

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

\[ \text {Solve}\left [\frac {1}{9} 2^{2/3} \left (\frac {\left (1-\frac {\left (x^2+x+3\right ) (x y(x)-2 x+3)}{x \sqrt [3]{\frac {\left (x^2+x+3\right )^3}{x^3}} (x y(x)+x+3)}\right ) \left (\frac {\left (x^2+x+3\right ) (x y(x)-2 x+3)}{x \sqrt [3]{\frac {\left (x^2+x+3\right )^3}{x^3}} (x y(x)+x+3)}+2\right ) \left (\left (1-\frac {\left (x^2+x+3\right ) (x y(x)-2 x+3)}{x \sqrt [3]{\frac {\left (x^2+x+3\right )^3}{x^3}} (x y(x)+x+3)}\right ) \log \left (2^{2/3} \left (1-\frac {\left (x^2+x+3\right ) (x y(x)-2 x+3)}{x \sqrt [3]{\frac {\left (x^2+x+3\right )^3}{x^3}} (x y(x)+x+3)}\right )\right )+\left (\frac {\left (x^2+x+3\right ) (x y(x)-2 x+3)}{x \sqrt [3]{\frac {\left (x^2+x+3\right )^3}{x^3}} (x y(x)+x+3)}-1\right ) \log \left (2^{2/3} \left (\frac {\left (x^2+x+3\right ) (x y(x)-2 x+3)}{x \sqrt [3]{\frac {\left (x^2+x+3\right )^3}{x^3}} (x y(x)+x+3)}+2\right )\right )-3\right )}{\frac {3 \left (x^2+x+3\right ) (x y(x)-2 x+3)}{x \sqrt [3]{\frac {\left (x^2+x+3\right )^3}{x^3}} (x y(x)+x+3)}-\frac {(x y(x)-2 x+3)^3}{(x y(x)+x+3)^3}-2}+\frac {x \left (\frac {\left (x^2+x+3\right )^3}{x^3}\right )^{2/3} \left (x^2+x \log (x)-3\right )}{\left (x^2+x+3\right )^2}\right )=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out