17.2.1 problem 1.1-3 (a)

Internal problem ID [3425]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.1-3, page 6
Problem number : 1.1-3 (a)
Date solved : Tuesday, March 04, 2025 at 04:38:20 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=2 y-4 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=5 \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 12

ode:=diff(y(t),t) = 2*y(t)-4; 
ic:=y(0) = 5; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = 2+3 \,{\mathrm e}^{2 t} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 14

ode=D[y[t],t]==2*y[t]-4; 
ic=y[0]==5; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to 3 e^{2 t}+2 \]

✓ Sympy. Time used: 0.112 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*y(t) + Derivative(y(t), t) + 4,0) 
ics = {y(0): 5} 
dsolve(ode,func=y(t),ics=ics)
 

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