Internal problem ID [5801]
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: 49.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {2 y+\left (y x^{2}+1\right ) x y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 16
dsolve(2*y(x)+(x^2*y(x)+1)*x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{\operatorname {LambertW}\left (\frac {c_{1}}{x^{2}}\right ) x^{2}} \]
✓ Solution by Mathematica
Time used: 60.405 (sec). Leaf size: 33
DSolve[2*y[x]+(x^2*y[x]+1)*x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{x^2 W\left (\frac {e^{\frac {1}{2} \left (-2-9 \sqrt [3]{-2} c_1\right )}}{x^2}\right )} \]