78.8.6 problem 6

Internal problem ID [18204]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 11:38:16 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 21

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

\[ y = \frac {\sqrt {-\frac {1}{\operatorname {LambertW}\left (-\frac {c_{1}}{x^{4}}\right )}}}{x} \]

✓ Solution by Mathematica

Time used: 7.635 (sec). Leaf size: 60

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

\begin{align*} y(x)\to -\frac {i}{x \sqrt {W\left (-\frac {e^{-2 c_1}}{x^4}\right )}} \\ y(x)\to \frac {i}{x \sqrt {W\left (-\frac {e^{-2 c_1}}{x^4}\right )}} \\ y(x)\to 0 \\ \end{align*}