74.11.56 problem 69

Internal problem ID [16306]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 69
Date solved : Tuesday, January 28, 2025 at 09:02:16 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+9 x&=\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: 0.017 (sec). Leaf size: 18

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

\[ x \left (t \right ) = \frac {\sin \left (3 t \right )}{18}-\frac {t \cos \left (3 t \right )}{6} \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 93

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

\[ x(t)\to \sin (3 t) \left (\int _1^t\frac {1}{6} \sin (6 K[2])dK[2]-\int _1^0\frac {1}{6} \sin (6 K[2])dK[2]\right )-\cos (3 t) \int _1^0-\frac {1}{3} \sin ^2(3 K[1])dK[1]+\cos (3 t) \int _1^t-\frac {1}{3} \sin ^2(3 K[1])dK[1] \]