7.19.13 problem 39

Internal problem ID [553]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 4. Laplace transform methods. Section 4.3 (Translation and partial fractions). Problems at page 296
Problem number : 39
Date solved : Saturday, March 29, 2025 at 04:56:30 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+9 x&=6 \cos \left (3 t \right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.093 (sec). Leaf size: 10

ode:=diff(diff(x(t),t),t)+9*x(t) = 6*cos(3*t); 
ic:=x(0) = 0, D(x)(0) = 0; 
dsolve([ode,ic],x(t),method='laplace');
 

\[ x = \sin \left (3 t \right ) t \]

✓ Mathematica. Time used: 0.082 (sec). Leaf size: 17

ode=D[x[t],{t,2}]+9*x[t]==6*Cos[3*t]; 
ic={x[0]==0,Derivative[1][x][0] ==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to t \sin (t) (2 \cos (2 t)+1) \]

✓ Sympy. Time used: 0.094 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(9*x(t) - 6*cos(3*t) + Derivative(x(t), (t, 2)),0) 
ics = {x(0): 0, Subs(Derivative(x(t), t), t, 0): 0} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = t \sin {\left (3 t \right )} \]