Internal problem ID [12696]
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: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x y \left (1-y\right )-2 y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(x*y(x)*(1-y(x))-2*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{1+{\mathrm e}^{-\frac {x^{2}}{4}} c_{1}} \]
✓ Solution by Mathematica
Time used: 0.392 (sec). Leaf size: 41
DSolve[x*y[x]*(1-y[x])-2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{\frac {x^2}{4}}}{e^{\frac {x^2}{4}}+e^{c_1}} \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}