5.31 problem 28

Internal problem ID [1005]

Book: Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number: 28.
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: 0.016 (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: 0.033 (sec). Leaf size: 36

DSolve[y'[x]==(x+y[x])/(x-y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+1\right )-\text {ArcTan}\left (\frac {y(x)}{x}\right )=-\log (x)+c_1,y(x)\right ] \]