Internal problem ID [264]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.6, Forced Oscillations and Resonance. Page 362
Problem number: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{\prime \prime }+3 x^{\prime }+5 x+4 \cos \left (5 t \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 43
dsolve(diff(x(t),t$2)+3*diff(x(t),t)+5*x(t)=-4*cos(5*t),x(t), singsol=all)
\[ x \relax (t ) = {\mathrm e}^{-\frac {3 t}{2}} \sin \left (\frac {\sqrt {11}\, t}{2}\right ) c_{2}+{\mathrm e}^{-\frac {3 t}{2}} \cos \left (\frac {\sqrt {11}\, t}{2}\right ) c_{1}-\frac {12 \sin \left (5 t \right )}{125}+\frac {16 \cos \left (5 t \right )}{125} \]
✓ Solution by Mathematica
Time used: 0.804 (sec). Leaf size: 60
DSolve[x''[t]+3*x'[t]+5*x[t]==-4*Cos[5*t],x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {4}{125} (4 \cos (5 t)-3 \sin (5 t))+e^{-3 t/2} \left (c_2 \cos \left (\frac {\sqrt {11} t}{2}\right )+c_1 \sin \left (\frac {\sqrt {11} t}{2}\right )\right ) \\ \end{align*}