Internal problem ID [14387]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-y-\left (6 t -2 y-3\right ) y^{\prime }=-3 t -1} \]
✓ Solution by Maple
Time used: 0.047 (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)
\[ y \left (t \right ) = -\frac {\operatorname {LambertW}\left (-2 \,{\mathrm e}^{5 t -4-5 c_{1}}\right )}{2}+3 t -2 \]
✓ Solution by Mathematica
Time used: 3.885 (sec). Leaf size: 35
DSolve[(3*t-y[t]+1)-(6*t-2*y[t]-3)*y'[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*}