71.7.11 problem 15

Internal problem ID [14432]
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
Date solved : Tuesday, January 28, 2025 at 06:30:54 AM
CAS classification : [_separable]

\begin{align*} x y \left (1-y\right )-2 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

dsolve(x*y(x)*(1-y(x))-2*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {1}{1+{\mathrm e}^{-\frac {x^{2}}{4}} c_{1}} \]

✓ Solution by Mathematica

Time used: 0.217 (sec). Leaf size: 46

DSolve[x*y[x]*(1-y[x])-2*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-1) K[1]}dK[1]\&\right ]\left [-\frac {x^2}{4}+c_1\right ] \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}