50.5.12 problem 4(b)

Internal problem ID [7882]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page 28
Problem number : 4(b)
Date solved : Monday, January 27, 2025 at 03:30:41 PM
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: 0.017 (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: 3.605 (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*}