Internal problem ID [4996]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems.
page 12
Problem number: 1.
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 {x -y+\left (x +y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 24
dsolve((x-y(x))+(x+y(x))*diff(y(x),x)=0,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: 0.054 (sec). Leaf size: 34
DSolve[(x-y[x])+(x+y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\text {ArcTan}\left (\frac {y(x)}{x}\right )+\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+1\right )=-\log (x)+c_1,y(x)\right ] \]