Internal problem ID [11717]
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: 14.1 (ix).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+2 x^{\prime }+10 x={\mathrm e}^{-t} \cos \left (3 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 43
dsolve(diff(x(t),t$2)+2*diff(x(t),t)+10*x(t)=exp(-t)*cos(3*t),x(t), singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{-t} \sin \left (3 t \right ) c_{2} +{\mathrm e}^{-t} \cos \left (3 t \right ) c_{1} +\frac {{\mathrm e}^{-t} \left (\cos \left (3 t \right )+3 t \sin \left (3 t \right )\right )}{18} \]
✓ Solution by Mathematica
Time used: 0.084 (sec). Leaf size: 38
DSolve[x''[t]+2*x'[t]+10*x[t]==Exp[-t]*Cos[3*t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{36} e^{-t} ((1+36 c_2) \cos (3 t)+6 (t+6 c_1) \sin (3 t)) \]