68.4.32 problem 32

Internal problem ID [17212]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 32
Date solved : Thursday, October 02, 2025 at 01:54:56 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.104 (sec). Leaf size: 42

ode=D[y[x],x]==y[x]^2-3*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]-2) (K[1]-1)}dK[1]\&\right ][x+c_1]\\ y(x)&\to 1\\ y(x)&\to 2 \end{align*}

✓ Sympy. Time used: 0.191 (sec). Leaf size: 17

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)
 

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