74.7.44 problem 42 (c)

Internal problem ID [16121]
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 : Tuesday, January 28, 2025 at 08:50:07 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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[(3*t-y[t]+1)-(6*t-2*y[t]-3)*D[y[t],t]==0,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*}