Internal problem ID [5764]
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]
\[ \boxed {x y+y^{2}-x^{2} y^{\prime }=-x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 11
dsolve((x^2+x*y(x)+y(x)^2)=x^2*diff(y(x),x),y(x), singsol=all)
\[ y \left (x \right ) = \tan \left (\ln \left (x \right )+c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 0.188 (sec). Leaf size: 13
DSolve[(x^2+x*y[x]+y[x]^2)==x^2*y'[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \tan (\log (x)+c_1) \]