Internal problem ID [1971]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 9, page 38
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {\left (x^{3} y^{3}-1\right ) y^{\prime }+x^{2} y^{4}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
dsolve((x^3*y(x)^3-1)*diff(y(x),x)+x^2*y(x)^4=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-c_{1}}}{\left (-\frac {x^{3} {\mathrm e}^{-3 c_{1}}}{\operatorname {LambertW}\left (-x^{3} {\mathrm e}^{-3 c_{1}}\right )}\right )^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 4.808 (sec). Leaf size: 90
DSolve[(x^3*y[x]^3-1)*y'[x]+x^2*y[x]^4==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt [3]{W\left (-e^{-3 c_1} x^3\right )}}{x} \\ y(x)\to \frac {\sqrt [3]{-1} \sqrt [3]{W\left (-e^{-3 c_1} x^3\right )}}{x} \\ y(x)\to -\frac {(-1)^{2/3} \sqrt [3]{W\left (-e^{-3 c_1} x^3\right )}}{x} \\ y(x)\to 0 \\ \end{align*}