Internal problem ID [12697]
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]
\[ \boxed {x \left (1-y^{3}\right )-3 y^{\prime } y^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 66
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 ({\mathrm e}^{-\frac {x^{2}}{2}} c_{1} +1\right )^{\frac {1}{3}} \\ y \left (x \right ) &= -\frac {\left ({\mathrm e}^{-\frac {x^{2}}{2}} c_{1} +1\right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2} \\ y \left (x \right ) &= \frac {\left ({\mathrm e}^{-\frac {x^{2}}{2}} c_{1} +1\right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{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*}