47.2.48 problem 44

Internal problem ID [7464]
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 : 44
Date solved : Monday, January 27, 2025 at 03:01:08 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y+x \left (2 y x +1\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 18

dsolve(y(x)+x*(2*x*y(x)+1)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {1}{2 \operatorname {LambertW}\left (\frac {c_{1}}{2 x}\right ) x} \]

✓ Solution by Mathematica

Time used: 60.495 (sec). Leaf size: 36

DSolve[y[x]+x*(2*x*y[x]+1)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2 x W\left (\frac {e^{\frac {1}{2} \left (-2-9 \sqrt [3]{-2} c_1\right )}}{x}\right )} \]