66.8.15 problem 28

Internal problem ID [16066]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Review Exercises for chapter 1. page 136
Problem number : 28
Date solved : Thursday, October 02, 2025 at 10:40:37 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.117 (sec). Leaf size: 42

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

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

✓ Sympy. Time used: 0.234 (sec). Leaf size: 12

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

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