Internal problem ID [266]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.6, Forced Oscillations and Resonance. Page 362
Problem number: 10.
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 }+3 x-8 \cos \left (10 t \right )-6 \sin \left (10 t \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 43
dsolve(diff(x(t),t$2)+3*diff(x(t),t)+3*x(t)=8*cos(10*t)+6*sin(10*t),x(t), singsol=all)
\[ x \relax (t ) = {\mathrm e}^{-\frac {3 t}{2}} \sin \left (\frac {\sqrt {3}\, t}{2}\right ) c_{2}+{\mathrm e}^{-\frac {3 t}{2}} \cos \left (\frac {\sqrt {3}\, t}{2}\right ) c_{1}-\frac {956 \cos \left (10 t \right )}{10309}-\frac {342 \sin \left (10 t \right )}{10309} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 60
DSolve[x''[t]+3*x'[t]+3*x[t]==8*Cos[10*t]+6*Sin[10*t],x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {2 (171 \sin (10 t)+478 \cos (10 t))}{10309}+e^{-3 t/2} \left (c_2 \cos \left (\frac {\sqrt {3} t}{2}\right )+c_1 \sin \left (\frac {\sqrt {3} t}{2}\right )\right ) \\ \end{align*}