74.7.44 problem 42 (c)

Internal problem ID [16042]
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 (c)
Date solved : Thursday, March 13, 2025 at 07:36:23 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.070 (sec). Leaf size: 23

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

\[ y = -\frac {\operatorname {LambertW}\left (-2 \,{\mathrm e}^{5 t -4-5 c_{1}}\right )}{2}+3 t -2 \]

✓ Mathematica. Time used: 3.123 (sec). Leaf size: 35

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

\begin{align*} y(t)\to -\frac {1}{2} W\left (-e^{5 t-1+c_1}\right )+3 t-2 \\ y(t)\to 3 t-2 \\ \end{align*}

✓ Sympy. Time used: 1.012 (sec). Leaf size: 19

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

\[ y{\left (t \right )} = 3 t - \frac {W\left (C_{1} e^{5 t - 4}\right )}{2} - 2 \]