72.3.12 problem 16

Internal problem ID [14597]
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 1.4 page 61
Problem number : 16
Date solved : Thursday, March 13, 2025 at 03:39:04 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 12

ode:=diff(y(t),t) = 2-y(t); 
ic:=y(0) = 1; 
dsolve([ode,ic],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 14

ode=D[y[t],t]==2-y[t]; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to 2-e^{-t} \]

✓ Sympy. Time used: 0.114 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) + Derivative(y(t), t) - 2,0) 
ics = {y(0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

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