Internal problem ID [12377]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.3.3, page 71
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x \left (1-y^{3}\right )-3 y^{2} y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 88
dsolve(x*(1-y(x)^3)-3*y(x)^2*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \left (1+c_{1} {\mathrm e}^{-\frac {x^{2}}{2}}\right )^{\frac {1}{3}} y \left (x \right ) = -\frac {\left (1+c_{1} {\mathrm e}^{-\frac {x^{2}}{2}}\right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (1+c_{1} {\mathrm e}^{-\frac {x^{2}}{2}}\right )^{\frac {1}{3}}}{2} y \left (x \right ) = -\frac {\left (1+c_{1} {\mathrm e}^{-\frac {x^{2}}{2}}\right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (1+c_{1} {\mathrm e}^{-\frac {x^{2}}{2}}\right )^{\frac {1}{3}}}{2} \end{align*}
✓ Solution by Mathematica
Time used: 2.121 (sec). Leaf size: 111
DSolve[x*(1-y[x]^3)-3*y[x]^2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt [3]{1+e^{-\frac {x^2}{2}+3 c_1}} y(x)\to -\sqrt [3]{-1} \sqrt [3]{1+e^{-\frac {x^2}{2}+3 c_1}} y(x)\to (-1)^{2/3} \sqrt [3]{1+e^{-\frac {x^2}{2}+3 c_1}} y(x)\to 1 y(x)\to -\sqrt [3]{-1} y(x)\to (-1)^{2/3} \end{align*}