17.6.3 problem 1.2-1 (c)

Internal problem ID [3440]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-1, page 12
Problem number : 1.2-1 (c)
Date solved : Tuesday, March 04, 2025 at 04:39:13 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=2 y+{\mathrm e}^{-3 t} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=diff(y(t),t) = 2*y(t)+exp(-3*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {\left (5 c_{1} {\mathrm e}^{5 t}-1\right ) {\mathrm e}^{-3 t}}{5} \]

✓ Mathematica. Time used: 0.069 (sec). Leaf size: 23

ode=D[y[t],t]==2*y[t]+Exp[-3*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to -\frac {e^{-3 t}}{5}+c_1 e^{2 t} \]

✓ Sympy. Time used: 0.145 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*y(t) + Derivative(y(t), t) - exp(-3*t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{2 t} - \frac {e^{- 3 t}}{5} \]