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 : Wednesday, February 05, 2025 at 03:45:47 AM
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*}

✓ Solution by Maple

Time used: 0.196 (sec). Leaf size: 10

dsolve([diff(x(t),t$2)+9*x(t)=6*cos(3*t),x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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