47.2.15 problem 15

Internal problem ID [7431]
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 : 15
Date solved : Monday, January 27, 2025 at 02:56:27 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.081 (sec). Leaf size: 17

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

\[ y = -x \operatorname {LambertW}\left (-\frac {{\mathrm e}^{-c_{1}}}{x}\right ) \]

✓ Solution by Mathematica

Time used: 2.108 (sec). Leaf size: 25

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

\begin{align*} y(x)\to -x W\left (-\frac {e^{-c_1}}{x}\right ) \\ y(x)\to 0 \\ \end{align*}