67.3.26 problem 4.6 (f)

Internal problem ID [16347]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.6 (f)
Date solved : Thursday, October 02, 2025 at 01:21:59 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=200 y-2 y^{2} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

ode:=diff(y(x),x) = 200*y(x)-2*y(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {100}{1+100 \,{\mathrm e}^{-200 x} c_1} \]

✓ Mathematica. Time used: 0.119 (sec). Leaf size: 42

ode=D[y[x],x]==200*y[x]-2*y[x]^2; 
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]-100) K[1]}dK[1]\&\right ][-2 x+c_1]\\ y(x)&\to 0\\ y(x)&\to 100 \end{align*}

✓ Sympy. Time used: 0.251 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x)**2 - 200*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {100}{C_{1} e^{- 200 x} + 1} \]