Internal problem ID [5508]
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. Problems for Review and Discovery. Page
53
Problem number: 2(e).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x +y}{x -y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.394 (sec). Leaf size: 30
dsolve([diff(y(x),x)=(x+y(x))/(x-y(x)),y(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {\sin \left (\RootOf \left (4 \textit {\_Z} -2 \ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )-4 \ln \relax (x )+2 \ln \relax (2)-\pi \right )\right ) x}{\cos \left (\RootOf \left (4 \textit {\_Z} -2 \ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )-4 \ln \relax (x )+2 \ln \relax (2)-\pi \right )\right )} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 46
DSolve[{y'[x]==(x+y[x])/(x-y[x]),{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+1\right )-\text {ArcTan}\left (\frac {y(x)}{x}\right )=\frac {1}{4} (2 \log (2)-\pi )-\log (x),y(x)\right ] \]