74.7.45 problem 42 (d)

Internal problem ID [16043]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 42 (d)
Date solved : Thursday, March 13, 2025 at 07:36:26 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 t +3 y+1+\left (4 t +6 y+1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.069 (sec). Leaf size: 23

ode:=2*t+3*y(t)+1+(4*t+6*y(t)+1)*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 4.073 (sec). Leaf size: 43

ode=(2*t+3*y[t]+1)+(4*t+6*y[t]+1)*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)\to \frac {1}{6} \left (3 W\left (-e^{\frac {t}{3}-1+c_1}\right )-4 t+2\right ) \\ y(t)\to \frac {1}{3} (1-2 t) \\ \end{align*}

✓ Sympy. Time used: 2.742 (sec). Leaf size: 107

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*t + (4*t + 6*y(t) + 1)*Derivative(y(t), t) + 3*y(t) + 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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