Internal problem ID [709]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.7 Forced Vibrations. page 217
Problem number: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u-3 \cos \left (6 t \right )=0} \end {gather*} With initial conditions \begin {align*} [u \relax (0) = 2, u^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.041 (sec). Leaf size: 46
dsolve([diff(u(t),t$2)+125/1000*diff(u(t),t)+4*u(t) = 3*cos(6*t),u(0) = 2, D(u)(0) = 0],u(t), singsol=all)
\[ u \relax (t ) = \frac {2806 \,{\mathrm e}^{-\frac {t}{16}} \sqrt {1023}\, \sin \left (\frac {\sqrt {1023}\, t}{16}\right )}{1524549}+\frac {34322 \,{\mathrm e}^{-\frac {t}{16}} \cos \left (\frac {\sqrt {1023}\, t}{16}\right )}{16393}-\frac {1536 \cos \left (6 t \right )}{16393}+\frac {36 \sin \left (6 t \right )}{16393} \]
✓ Solution by Mathematica
Time used: 1.352 (sec). Leaf size: 63
DSolve[{u''[t]+125/1000*u'[t]+4*u[t] ==3*Cos[6*t],{u[0]==0,u'[0]==0}},u[t],t,IncludeSingularSolutions -> True]
\begin{align*} u(t)\to \frac {4 \left (3069 \sin (6 t)-130944 \cos (6 t)+32 e^{-t/16} \left (4092 \cos \left (\frac {\sqrt {1023} t}{16}\right )-5 \sqrt {1023} \sin \left (\frac {\sqrt {1023} t}{16}\right )\right )\right )}{5590013} \\ \end{align*}