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(a).
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: 0.033 (sec). Leaf size: 31
dsolve(diff(y(x),x)=(x+y(x)+4)/(x-y(x)-6),y(x), singsol=all)
\[ y \relax (x ) = -5-\tan \left (\RootOf \left (2 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \left (x -1\right )+2 c_{1}\right )\right ) \left (x -1\right ) \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 58
DSolve[y'[x]==(x+y[x]+4)/(x-y[x]-6),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \text {ArcTan}\left (\frac {y(x)+x+4}{y(x)-x+6}\right )+\log \left (\frac {x^2+y(x)^2+10 y(x)-2 x+26}{2 (x-1)^2}\right )+2 \log (x-1)+c_1=0,y(x)\right ] \]