Internal problem ID [5318]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 5. Existence and uniqueness of solutions to first order equations. Page
190
Problem number: 4(a).
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*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 24
dsolve(diff(y(x),x)=(x+y(x))/(x-y(x)),y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\RootOf \left (-2 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \relax (x )+2 c_{1}\right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 36
DSolve[y'[x]==(x+y[x])/(x-y[x]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+1\right )-\text {ArcTan}\left (\frac {y(x)}{x}\right )=-\log (x)+c_1,y(x)\right ] \]