26.5.11 problem 14

Internal problem ID [4285]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, End of chapter, page 61
Problem number : 14
Date solved : Sunday, March 30, 2025 at 02:50:54 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: 0.019 (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: 3.924 (sec). Leaf size: 34

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

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

✓ Sympy. Time used: 1.295 (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)
 

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