26.3.5 problem 4(b)

Internal problem ID [4265]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 10, page 47
Problem number : 4(b)
Date solved : Monday, January 27, 2025 at 08:46:59 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 3.684 (sec). Leaf size: 76

DSolve[y[x]-(x+x*y[x]^3)*D[y[x],x]==0,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*}