81.7.9 problem 8-8

Internal problem ID [21583]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 8. Riccati Equation. Page 124.
Problem number : 8-8
Date solved : Thursday, October 02, 2025 at 07:58:39 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=-2+3 y-y^{2} \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 20

ode:=diff(y(x),x) = -2+3*y(x)-y(x)^2; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.486 (sec). Leaf size: 40

ode=D[y[x],x]== -2+3*y[x]-y[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2 e^x-e^{c_1}}{e^x-e^{c_1}}\\ y(x)&\to 1\\ y(x)&\to 2 \end{align*}

✓ Sympy. Time used: 0.190 (sec). Leaf size: 15

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

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