74.22.15 problem 15

Internal problem ID [16662]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 6. Systems of Differential Equations. Exercises 6.1, page 282
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 09:16:26 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+16 x&=t \sin \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 26

dsolve(diff(x(t),t$2)+16*x(t)=t*sin(t),x(t), singsol=all)
 

\[ x \left (t \right ) = \sin \left (4 t \right ) c_{2} +\cos \left (4 t \right ) c_{1} -\frac {2 \cos \left (t \right )}{225}+\frac {t \sin \left (t \right )}{15} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 33

DSolve[D[x[t],{t,2}]+16*x[t]==t*Sin[t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{15} t \sin (t)-\frac {2 \cos (t)}{225}+c_1 \cos (4 t)+c_2 \sin (4 t) \]