78.3.14 problem 5 (b)

Internal problem ID [18117]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 7 (Homogeneous Equations). Problems at page 67
Problem number : 5 (b)
Date solved : Tuesday, January 28, 2025 at 11:28:55 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {x +y+4}{x +y-6} \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 21

dsolve(diff(y(x),x)=(x+y(x)+4)/(x+y(x)-6),y(x), singsol=all)
 

\[ y = -x -5 \operatorname {LambertW}\left (-\frac {c_1 \,{\mathrm e}^{-\frac {2 x}{5}+\frac {1}{5}}}{5}\right )+1 \]

✓ Solution by Mathematica

Time used: 3.589 (sec). Leaf size: 35

DSolve[D[y[x],x]==(x+y[x]+4)/(x+y[x]-6),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -5 W\left (-e^{-\frac {2 x}{5}-1+c_1}\right )-x+1 \\ y(x)\to 1-x \\ \end{align*}