78.8.14 problem 14

Internal problem ID [18133]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 14
Date solved : Thursday, March 13, 2025 at 11:40:09 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 15

ode:=6*x+4*y(x)+3+(3*x+2*y(x)+2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 60.304 (sec). Leaf size: 4714

ode=(6*x+4*y[x]+3)+(3*x+2*y[x]+2)*D[y[x],x]+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✓ Sympy. Time used: 1.302 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*x + (3*x + 2*y(x) + 2)*Derivative(y(x), x) + 4*y(x) + 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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