65.7.13 problem 14.3

Internal problem ID [13777]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 14, Inhomogeneous second order linear equations. Exercises page 140
Problem number : 14.3
Date solved : Tuesday, January 28, 2025 at 06:03:12 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+4 x&=289 t \,{\mathrm e}^{t} \sin \left (2 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 36

dsolve(diff(x(t),t$2)+4*x(t)=289*t*exp(t)*sin(2*t),x(t), singsol=all)
 

\[ x \left (t \right ) = \left (\left (-68 t +76\right ) {\mathrm e}^{t}+c_{1} \right ) \cos \left (2 t \right )+17 \sin \left (2 t \right ) \left ({\mathrm e}^{t} \left (t -\frac {2}{17}\right )+\frac {c_{2}}{17}\right ) \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 40

DSolve[D[x[t],{t,2}]+4*x[t]==289*t*Exp[t]*Sin[2*t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \left (e^t (76-68 t)+c_1\right ) \cos (2 t)+\left (e^t (17 t-2)+c_2\right ) \sin (2 t) \]