Internal problem ID [267]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.6, Forced Oscillations and Resonance. Page 362
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{\prime \prime }+4 x^{\prime }+5 x-10 \cos \left (3 t \right )=0} \end {gather*} With initial conditions \begin {align*} [x \relax (0) = 0, x^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve([diff(x(t),t$2)+4*diff(x(t),t)+5*x(t)=10*cos(3*t),x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
\[ x \relax (t ) = \frac {\left (\cos \relax (t )-7 \sin \relax (t )\right ) {\mathrm e}^{-2 t}}{4}-\frac {\cos \left (3 t \right )}{4}+\frac {3 \sin \left (3 t \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 35
DSolve[{x''[t]+4*x'[t]+5*x[t]==10*Cos[3*t],{x[0]==0,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{4} \left (3 \sin (3 t)-\cos (3 t)+e^{-2 t} (\cos (t)-7 \sin (t))\right ) \\ \end{align*}