Internal problem ID [14220]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {x +y+3}{3 x +3 y+1}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 23
dsolve(diff(y(x),x)=(x+y(x)+3)/(3*x+3*y(x)+1),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {2 \operatorname {LambertW}\left (-\frac {3 \,{\mathrm e}^{-2 x -\frac {3}{2}+2 c_{1}}}{2}\right )}{3}-x -1 \]
✓ Solution by Mathematica
Time used: 3.699 (sec). Leaf size: 35
DSolve[y'[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*}