20.21.4 problem Problem 4

Internal problem ID [3931]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 10, The Laplace Transform and Some Elementary Applications. Exercises for 10.4. page 689
Problem number : Problem 4
Date solved : Tuesday, March 04, 2025 at 05:19:39 PM
CAS classification : [[_linear, `class A`]]

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

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Maple. Time used: 2.513 (sec). Leaf size: 15

ode:=diff(y(t),t)+2*y(t) = 4*t; 
ic:=y(0) = 1; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = 2 \,{\mathrm e}^{-2 t}+2 t -1 \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 17

ode=D[y[t],t]+2*y[t]==4*t; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to 2 t+2 e^{-2 t}-1 \]

✓ Sympy. Time used: 0.142 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-4*t + 2*y(t) + Derivative(y(t), t),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 2 t - 1 + 2 e^{- 2 t} \]