20.21.9 problem Problem 9

Internal problem ID [3936]
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 9
Date solved : Tuesday, March 04, 2025 at 05:19:44 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+4 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Maple. Time used: 2.843 (sec). Leaf size: 17

ode:=diff(diff(y(t),t),t)+4*y(t) = 0; 
ic:=y(0) = 5, D(y)(0) = 1; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = 5 \cos \left (2 t \right )+\frac {\sin \left (2 t \right )}{2} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 17

ode=D[y[t],{t,2}]+4*y[t]==0; 
ic={y[0]==5,Derivative[1][y][0] ==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to 5 \cos (2 t)+\sin (t) \cos (t) \]

✓ Sympy. Time used: 0.066 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*y(t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 5, Subs(Derivative(y(t), t), t, 0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {\sin {\left (2 t \right )}}{2} + 5 \cos {\left (2 t \right )} \]