20.21.25 problem Problem 25

Internal problem ID [3952]
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 25
Date solved : Tuesday, March 04, 2025 at 05:19:58 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=9 \sin \left (t \right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 2.823 (sec). Leaf size: 19

ode:=diff(diff(y(t),t),t)+4*y(t) = 9*sin(t); 
ic:=y(0) = 1, D(y)(0) = -1; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = 3 \sin \left (t \right )+\cos \left (2 t \right )-2 \sin \left (2 t \right ) \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 20

ode=D[y[t],{t,2}]+4*y[t]==9*Sin[t]; 
ic={y[0]==1,Derivative[1][y][0] ==-1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to 3 \sin (t)-2 \sin (2 t)+\cos (2 t) \]

✓ Sympy. Time used: 0.082 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*y(t) - 9*sin(t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(t), t), t, 0): -1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 3 \sin {\left (t \right )} - 2 \sin {\left (2 t \right )} + \cos {\left (2 t \right )} \]