Internal problem ID [271]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.6, Forced Oscillations and Resonance. Page 362
Problem number: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{\prime \prime }+8 x^{\prime }+25 x-200 \cos \relax (t )-520 \sin \relax (t )=0} \end {gather*} With initial conditions \begin {align*} [x \relax (0) = -30, x^{\prime }\relax (0) = -10] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve([diff(x(t),t$2)+8*diff(x(t),t)+25*x(t)=200*cos(t)+520*sin(t),x(0) = -30, D(x)(0) = -10],x(t), singsol=all)
\[ x \relax (t ) = \left (-31 \cos \left (3 t \right )-52 \sin \left (3 t \right )\right ) {\mathrm e}^{-4 t}+\cos \relax (t )+22 \sin \relax (t ) \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 32
DSolve[{x''[t]+8*x'[t]+25*x[t]==200*Cos[t]+520*Sin[t],{x[0]==-30,x'[0]==-10}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 22 \sin (t)+\cos (t)-e^{-4 t} (52 \sin (3 t)+31 \cos (3 t)) \\ \end{align*}