20.21.6 problem Problem 6

Internal problem ID [3933]
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 6
Date solved : Tuesday, March 04, 2025 at 05:19:41 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y&=5 \sin \left (2 t \right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 2.696 (sec). Leaf size: 19

ode:=diff(y(t),t)-y(t) = 5*sin(2*t); 
ic:=y(0) = -1; 
dsolve([ode,ic],y(t),method='laplace');
 

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

✓ Mathematica. Time used: 0.047 (sec). Leaf size: 21

ode=D[y[t],t]-y[t]==5*Sin[2*t]; 
ic={y[0]==-1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^t-\sin (2 t)-2 \cos (2 t) \]

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

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t) - 5*sin(2*t) + Derivative(y(t), t),0) 
ics = {y(0): -1} 
dsolve(ode,func=y(t),ics=ics)
 

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