78.6.10 problem 4.a

Internal problem ID [21073]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 7, Nonlinear systems. Problems section 7.11
Problem number : 4.a
Date solved : Thursday, October 02, 2025 at 07:03:20 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.221 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to \frac {e^x}{\mu e^x+e^{c_1}}\\ y(x)&\to 0\\ y(x)&\to \frac {1}{\mu } \end{align*}

✓ Sympy. Time used: 0.243 (sec). Leaf size: 12

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

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