15.8.11 problem 11

Internal problem ID [3014]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 11
Date solved : Monday, January 27, 2025 at 07:08:32 AM
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: 0.020 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 7.268 (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*}