72.1.5 problem 8

Internal problem ID [14526]
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. Exercises section 1.2. page 33
Problem number : 8
Date solved : Thursday, March 13, 2025 at 03:32:20 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 12

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

\[ y = 2+{\mathrm e}^{-t} c_{1} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 20

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

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

✓ Sympy. Time used: 0.111 (sec). Leaf size: 8

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

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