47.2.4 problem 4

Internal problem ID [7420]
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 : 4
Date solved : Monday, January 27, 2025 at 02:53:49 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{2}+x^{2} y^{\prime }&=x y y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 2.177 (sec). Leaf size: 25

DSolve[y[x]^2+x^2*D[y[x],x]==x*y[x]*D[y[x],x],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*}