3.5 problem 4(b)

Internal problem ID [2595]

Book: Differential equations with applications and historial notes, George F. Simmons, 1971
Section: Chapter 2, section 10, page 47
Problem number: 4(b).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

Solve \begin {gather*} \boxed {y-\left (x +x y^{3}\right ) y^{\prime }=0} \end {gather*}

Solution by Maple

Time used: 0.018 (sec). Leaf size: 20

dsolve(y(x)-(x+x*y(x)^3)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \relax (x ) = x \,{\mathrm e}^{-\frac {\LambertW \left (x^{3} {\mathrm e}^{3 c_{1}}\right )}{3}+c_{1}} \]

Solution by Mathematica

Time used: 30.071 (sec). Leaf size: 76

DSolve[y[x]-(x+x*y[x]^3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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