71.7.11 problem 15

Internal problem ID [14361]
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 : Monday, March 31, 2025 at 12:19:22 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

\[ y = \frac {1}{1+{\mathrm e}^{-\frac {x^{2}}{4}} c_1} \]

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

ode=x*y[x]*(1-y[x])-2*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},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*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(1 - y(x))*y(x) - 2*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out