71.6.7 problem 7

Internal problem ID [14342]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.2, page 63
Problem number : 7
Date solved : Monday, March 31, 2025 at 12:18:30 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=-2 y+y^{2} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.056 (sec). Leaf size: 14

ode:=diff(y(x),x) = -2*y(x)+y(x)^2; 
ic:=y(0) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 16

ode=D[y[x],x]==-2*y[x]+y[x]^2; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {2}{e^{2 x}+1} \]

✓ Sympy. Time used: 0.343 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = - \frac {2}{- e^{2 x} - 1} \]