Internal problem ID [263]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.6, Forced Oscillations and Resonance. Page 362
Problem number: 7.
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 }+4 x-10 \cos \left (3 t \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 30
dsolve(diff(x(t),t$2)+4*diff(x(t),t)+4*x(t)=10*cos(3*t),x(t), singsol=all)
\[ x \relax (t ) = {\mathrm e}^{-2 t} c_{2}+{\mathrm e}^{-2 t} t c_{1}-\frac {50 \cos \left (3 t \right )}{169}+\frac {120 \sin \left (3 t \right )}{169} \]
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 36
DSolve[x''[t]+4*x'[t]+4*x[t]==10*Cos[3*t],x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {10}{169} (5 \cos (3 t)-12 \sin (3 t))+e^{-2 t} (c_2 t+c_1) \\ \end{align*}