78.6.8 problem 3.c

Internal problem ID [21071]
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 : 3.c
Date solved : Thursday, October 02, 2025 at 07:03:19 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&={\frac {3}{2}} \\ \end{align*}

✓ Maple. Time used: 0.035 (sec). Leaf size: 14

ode:=diff(y(x),x) = y(x)-y(x)^2; 
ic:=[y(0) = 3/2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {3}{{\mathrm e}^{-x}-3} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 19

ode=D[y[x],x]==y[x]-y[x]^2; 
ic={y[0]==15/10}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {3 e^x}{3 e^x-1} \end{align*}

✓ Sympy. Time used: 0.214 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)**2 - y(x) + Derivative(y(x), x),0) 
ics = {y(0): 3/2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {1}{1 - \frac {e^{- x}}{3}} \]