11.7.1 problem 1.2-2 (a)

Internal problem ID [3447]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-2, page 12
Problem number : 1.2-2 (a)
Date solved : Tuesday, September 30, 2025 at 06:38:38 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 8

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

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 10

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

\begin{align*} y(t)&\to 2 e^t \end{align*}

✓ Sympy. Time used: 0.023 (sec). Leaf size: 7

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

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