Internal problem ID [11718]
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 (x).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+6 x^{\prime }+10 x={\mathrm e}^{-2 t} \cos \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(x(t),t$2)+6*diff(x(t),t)+10*x(t)=exp(-2*t)*cos(t),x(t), singsol=all)
\[ x \left (t \right ) = \sin \left (t \right ) {\mathrm e}^{-3 t} c_{2} +\cos \left (t \right ) {\mathrm e}^{-3 t} c_{1} +\frac {{\mathrm e}^{-2 t} \left (\cos \left (t \right )+2 \sin \left (t \right )\right )}{5} \]
✓ Solution by Mathematica
Time used: 0.087 (sec). Leaf size: 33
DSolve[x''[t]+6*x'[t]+10*x[t]==Exp[-3*t]*Cos[t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{2} e^{-3 t} ((1+2 c_2) \cos (t)+(t+2 c_1) \sin (t)) \]