90.8.5 problem 5

Internal problem ID [25179]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 2. The Laplace Transform. Exercises at page 109
Problem number : 5
Date solved : Thursday, October 02, 2025 at 11:57:36 PM
CAS classification : [[_linear, `class A`]]

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

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.036 (sec). Leaf size: 11

ode:=diff(y(t),t)+2*y(t) = 3*exp(t); 
ic:=[y(0) = 2]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

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

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 14

ode=D[y[t],t]+2*y[t]==3*Exp[t]; 
ic={y[0]==2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.077 (sec). Leaf size: 12

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

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