15.5.6 problem 6

Internal problem ID [2942]
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
Date solved : Monday, January 27, 2025 at 06:59:53 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} \left (x^{3} y^{3}-1\right ) y^{\prime }+x^{2} y^{4}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (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)
 

\[ y = \frac {{\mathrm e}^{-c_1}}{\left (-\frac {x^{3} {\mathrm e}^{-3 c_1}}{\operatorname {LambertW}\left (-x^{3} {\mathrm e}^{-3 c_1}\right )}\right )^{{1}/{3}}} \]

✓ Solution by Mathematica

Time used: 4.437 (sec). Leaf size: 90

DSolve[(x^3*y[x]^3-1)*D[y[x],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*}