Internal problem ID [5461]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x +y+4}{x +y-6}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 21
dsolve(diff(y(x),x)=(x+y(x)+4)/(x+y(x)-6),y(x), singsol=all)
\[ y \relax (x ) = -x -5 \LambertW \left (-\frac {{\mathrm e}^{-\frac {2 x}{5}} c_{1} {\mathrm e}^{\frac {1}{5}}}{5}\right )+1 \]
✓ Solution by Mathematica
Time used: 60.034 (sec). Leaf size: 26
DSolve[y'[x]==(x+y[x]+4)/(x+y[x]-6),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -5 \text {ProductLog}\left (-e^{-\frac {2 x}{5}-1+c_1}\right )-x+1 \\ \end{align*}