Internal problem ID [5011]
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: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Riccati]
Solve \begin {gather*} \boxed {x^{2}+y x +y^{2}-y^{\prime } x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve((x^2+x*y(x)+y(x)^2)=x^2*diff(y(x),x),y(x), singsol=all)
\[ y \relax (x ) = \tan \left (c_{1}+\ln \relax (x )\right ) x \]
✓ Solution by Mathematica
Time used: 0.311 (sec). Leaf size: 13
DSolve[(x^2+x*y[x]+y[x]^2)==x^2*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \tan (\log (x)+c_1) \\ \end{align*}