Internal problem ID [268]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.6, Forced Oscillations and Resonance. Page 362
Problem number: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{\prime \prime }+6 x^{\prime }+13 x-10 \sin \left (5 t \right )=0} \end {gather*} With initial conditions \begin {align*} [x \relax (0) = 0, x^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 37
dsolve([diff(x(t),t$2)+6*diff(x(t),t)+13*x(t)=10*sin(5*t),x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
\[ x \relax (t ) = \frac {\left (50 \cos \left (2 t \right )+125 \sin \left (2 t \right )\right ) {\mathrm e}^{-3 t}}{174}-\frac {25 \cos \left (5 t \right )}{87}-\frac {10 \sin \left (5 t \right )}{87} \]
✓ Solution by Mathematica
Time used: 0.156 (sec). Leaf size: 45
DSolve[{x''[t]+6*x'[t]+13*x[t]==10*Sin[5*t],{x[0]==0,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {5}{174} \left (5 e^{-3 t} (5 \sin (2 t)+2 \cos (2 t))-2 (2 \sin (5 t)+5 \cos (5 t))\right ) \\ \end{align*}