Internal problem ID [270]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.6, Forced Oscillations and Resonance. Page 362
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{\prime \prime }+2 x^{\prime }+26 x-600 \cos \left (10 t \right )=0} \end {gather*} With initial conditions \begin {align*} [x \relax (0) = 10, x^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 36
dsolve([diff(x(t),t$2)+2*diff(x(t),t)+26*x(t)=600*cos(10*t),x(0) = 10, D(x)(0) = 0],x(t), singsol=all)
\[ x \relax (t ) = \frac {\left (25790 \cos \left (5 t \right )-842 \sin \left (5 t \right )\right ) {\mathrm e}^{-t}}{1469}-\frac {11100 \cos \left (10 t \right )}{1469}+\frac {3000 \sin \left (10 t \right )}{1469} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 45
DSolve[{x''[t]+2*x'[t]+26*x[t]==600*Cos[10*t],{x[0]==10,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {e^{-t} \left (-842 \sin (5 t)+25790 \cos (5 t)-300 e^t (37 \cos (10 t)-10 \sin (10 t))\right )}{1469} \\ \end{align*}