Internal problem ID [3104]
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]
\[ \boxed {y-\left (x +y^{3} x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(y(x)-(x+x*y(x)^3)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{{\left (\frac {1}{\operatorname {LambertW}\left (c_{1} x^{3}\right )}\right )}^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 4.377 (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]{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*}