82.12.13 problem Ex. 13

Internal problem ID [18778]
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. Examples on chapter II at page 29
Problem number : Ex. 13
Date solved : Tuesday, January 28, 2025 at 12:16:55 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 6.989 (sec). Leaf size: 80

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

\begin{align*} y(x)\to \frac {x}{\sqrt [3]{W\left (e^{-3 c_1} x^3\right )}} \\ y(x)\to -\frac {\sqrt [3]{-1} x}{\sqrt [3]{W\left (e^{-3 c_1} x^3\right )}} \\ y(x)\to \frac {(-1)^{2/3} x}{\sqrt [3]{W\left (e^{-3 c_1} x^3\right )}} \\ y(x)\to 0 \\ \end{align*}