8.12.2 problem 2

Internal problem ID [909]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.6, Forced Oscillations and Resonance. Page 362
Problem number : 2
Date solved : Wednesday, February 05, 2025 at 04:44:13 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+4 x&=5 \sin \left (3 t \right ) \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 17

dsolve([diff(x(t),t$2)+4*x(t)=5*sin(3*t),x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {3 \sin \left (2 t \right )}{2}-\sin \left (3 t \right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 18

DSolve[{D[x[t],{t,2}]+4*x[t]==5*Sin[3*t],{x[0]==0,Derivative[1][x][0 ]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to 3 \sin (t) \cos (t)-\sin (3 t) \]