Internal problem ID [2043]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 16
dsolve((x^2*y(x))-(x^3+y(x)^3)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\left (\frac {1}{\operatorname {LambertW}\left (c_{1} x^{3}\right )}\right )}^{\frac {1}{3}} x \]
✓ Solution by Mathematica
Time used: 7.211 (sec). Leaf size: 80
DSolve[(x^2*y[x])-(x^3+y[x]^3)*y'[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*}