74.4.62 problem 60 (a)

Internal problem ID [15955]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 60 (a)
Date solved : Tuesday, January 28, 2025 at 08:24:36 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {x +y+3}{3 x +3 y+1} \end{align*}

✓ Solution by Maple

Time used: 0.063 (sec). Leaf size: 23

dsolve(diff(y(x),x)=(x+y(x)+3)/(3*x+3*y(x)+1),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 3.230 (sec). Leaf size: 35

DSolve[D[y[x],x]==(x+y[x]+3)/(3*x+3*y[x]+1),y[x],x,IncludeSingularSolutions -> True]
 

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