72.8.8 problem 21

Internal problem ID [14701]
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 : 21
Date solved : Monday, March 31, 2025 at 12:54:25 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

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

\[ y = \frac {3}{2}+{\mathrm e}^{-2 t} c_1 \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 24

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

\begin{align*} y(t)\to \frac {3}{2}+c_1 e^{-2 t} \\ y(t)\to \frac {3}{2} \\ \end{align*}

✓ Sympy. Time used: 0.111 (sec). Leaf size: 12

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

\[ y{\left (t \right )} = C_{1} e^{- 2 t} + \frac {3}{2} \]