17.5.1 problem 1.1-6 (a)

Internal problem ID [3434]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.1-6, page 7
Problem number : 1.1-6 (a)
Date solved : Tuesday, March 04, 2025 at 04:38:42 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y-1 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 10

ode:=diff(y(t),t) = y(t)-1; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 18

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

\begin{align*} y(t)\to 1+c_1 e^t \\ y(t)\to 1 \\ \end{align*}

✓ Sympy. Time used: 0.099 (sec). Leaf size: 8

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

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