50.5.11 problem 4(a)

Internal problem ID [7881]
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(a)
Date solved : Monday, January 27, 2025 at 03:30:38 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: 0.029 (sec). Leaf size: 31

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

\[ y = -5-\tan \left (\operatorname {RootOf}\left (2 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x -1\right )+2 c_{1} \right )\right ) \left (x -1\right ) \]

✓ Solution by Mathematica

Time used: 0.058 (sec). Leaf size: 58

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

\[ \text {Solve}\left [2 \arctan \left (\frac {y(x)+x+4}{y(x)-x+6}\right )+\log \left (\frac {x^2+y(x)^2+10 y(x)-2 x+26}{2 (x-1)^2}\right )+2 \log (x-1)+c_1=0,y(x)\right ] \]