68.4.62 problem 60 (a)

Internal problem ID [17242]
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 : Thursday, October 02, 2025 at 01:59:40 PM
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*}

✓ Maple. Time used: 0.026 (sec). Leaf size: 23

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

\[ y = -\frac {2 \operatorname {LambertW}\left (-\frac {3 \,{\mathrm e}^{-2 x -\frac {3}{2}+2 c_1}}{2}\right )}{3}-x -1 \]

✓ Mathematica. Time used: 2.131 (sec). Leaf size: 35

ode=D[y[x],x]==(x+y[x]+3)/(3*x+3*y[x]+1); 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.776 (sec). Leaf size: 24

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

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