20.21.5 problem Problem 5

Internal problem ID [3932]
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 5
Date solved : Tuesday, March 04, 2025 at 05:19:40 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y&=6 \cos \left (t \right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 2.685 (sec). Leaf size: 17

ode:=diff(y(t),t)-y(t) = 6*cos(t); 
ic:=y(0) = 2; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = -3 \cos \left (t \right )+3 \sin \left (t \right )+5 \,{\mathrm e}^{t} \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 19

ode=D[y[t],t]-y[t]==6*Cos[t]; 
ic={y[0]==2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to 5 e^t+3 \sin (t)-3 \cos (t) \]

✓ Sympy. Time used: 0.127 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t) - 6*cos(t) + Derivative(y(t), t),0) 
ics = {y(0): 2} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 5 e^{t} + 3 \sin {\left (t \right )} - 3 \cos {\left (t \right )} \]