Internal problem ID [5460]
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`]]
\[ \boxed {y^{\prime }-\frac {x +y+4}{x +y-6}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve(diff(y(x),x)=(x+y(x)+4)/(x+y(x)-6),y(x), singsol=all)
\[ y \left (x \right ) = -x -5 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{-\frac {2 x}{5}} c_{1} {\mathrm e}^{\frac {1}{5}}}{5}\right )+1 \]
✓ Solution by Mathematica
Time used: 3.76 (sec). Leaf size: 35
DSolve[y'[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*}