78.5.13 problem 4 (b)

Internal problem ID [18156]
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. Section 9 (Integrating Factors). Problems at page 80
Problem number : 4 (b)
Date solved : Tuesday, January 28, 2025 at 11:34:23 AM
CAS classification : [_separable]

\begin{align*} y-x y^{\prime }&=x y^{3} y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 3.596 (sec). Leaf size: 76

DSolve[y[x]-x*D[y[x],x] == x*y[x]^3*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \sqrt [3]{W\left (e^{3 c_1} x^3\right )} \\ y(x)\to -\sqrt [3]{-1} \sqrt [3]{W\left (e^{3 c_1} x^3\right )} \\ y(x)\to (-1)^{2/3} \sqrt [3]{W\left (e^{3 c_1} x^3\right )} \\ y(x)\to 0 \\ \end{align*}