82.7.1 problem Ex. 1

Internal problem ID [18747]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 24
Problem number : Ex. 1
Date solved : Tuesday, January 28, 2025 at 12:14:15 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x^{2} y-2 x y^{2}-\left (x^{3}-3 x^{2} y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 19

dsolve((x^2*y(x)-2*x*y(x)^2)-(x^3-3*x^2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {x}{3 \operatorname {LambertW}\left (-\frac {x^{{1}/{3}} {\mathrm e}^{\frac {c_{1}}{3}}}{3}\right )} \]

✓ Solution by Mathematica

Time used: 4.312 (sec). Leaf size: 35

DSolve[(x^2*y[x]-2*x*y[x]^2)-(x^3-3*x^2*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {x}{3 W\left (-\frac {1}{3} e^{-\frac {c_1}{3}} \sqrt [3]{x}\right )} \\ y(x)\to 0 \\ \end{align*}