Internal problem ID [11721]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+4 x=289 t \,{\mathrm e}^{t} \sin \left (2 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 48
dsolve(diff(x(t),t$2)+4*x(t)=289*t*exp(t)*sin(2*t),x(t), singsol=all)
\[ x \left (t \right ) = c_{2} \sin \left (2 t \right )+c_{1} \cos \left (2 t \right )-{\mathrm e}^{t} \left (68 \cos \left (2 t \right ) t -17 t \sin \left (2 t \right )-76 \cos \left (2 t \right )+2 \sin \left (2 t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 40
DSolve[x''[t]+4*x[t]==289*t*Exp[t]*Sin[2*t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \left (e^t (76-68 t)+c_1\right ) \cos (2 t)+\left (e^t (17 t-2)+c_2\right ) \sin (2 t) \]