Internal problem ID [14388]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {3 y+\left (4 t +6 y+1\right ) y^{\prime }=-2 t -1} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 23
dsolve((2*t+3*y(t)+1)+(4*t+6*y(t)+1)*diff(y(t),t)=0,y(t), singsol=all)
\[ y \left (t \right ) = \frac {\operatorname {LambertW}\left (\frac {2 \,{\mathrm e}^{-\frac {2}{3}+\frac {t}{3}-\frac {c_{1}}{3}}}{3}\right )}{2}+\frac {1}{3}-\frac {2 t}{3} \]
✓ Solution by Mathematica
Time used: 5.178 (sec). Leaf size: 43
DSolve[(2*t+3*y[t]+1)+(4*t+6*y[t]+1)*y'[t]==0,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*}