20.21.19 problem Problem 19

Internal problem ID [3946]
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 19
Date solved : Tuesday, March 04, 2025 at 05:19:52 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-9 y&=13 \sin \left (2 t \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Maple. Time used: 2.638 (sec). Leaf size: 21

ode:=diff(diff(y(t),t),t)-9*y(t) = 13*sin(2*t); 
ic:=y(0) = 3, D(y)(0) = 1; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = {\mathrm e}^{-3 t}+2 \,{\mathrm e}^{3 t}-\sin \left (2 t \right ) \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 24

ode=D[y[t],{t,2}]-9*y[t]==13*Sin[2*t]; 
ic={y[0]==3,Derivative[1][y][0] ==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-3 t}+2 e^{3 t}-\sin (2 t) \]

✓ Sympy. Time used: 0.092 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-9*y(t) - 13*sin(2*t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 3, Subs(Derivative(y(t), t), t, 0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

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