Internal problem ID [707]
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: 21.
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 (\frac {t}{4}\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: 0.049 (sec). Leaf size: 46
dsolve([diff(u(t),t$2)+125/1000*diff(u(t),t)+4*u(t) = 3*cos(t/4),u(0) = 2, D(u)(0) = 0],u(t), singsol=all)
\[ u \relax (t ) = \frac {19274 \,{\mathrm e}^{-\frac {t}{16}} \sqrt {1023}\, \sin \left (\frac {\sqrt {1023}\, t}{16}\right )}{16242171}+\frac {19658 \,{\mathrm e}^{-\frac {t}{16}} \cos \left (\frac {\sqrt {1023}\, t}{16}\right )}{15877}+\frac {12096 \cos \left (\frac {t}{4}\right )}{15877}+\frac {96 \sin \left (\frac {t}{4}\right )}{15877} \]
✓ Solution by Mathematica
Time used: 0.689 (sec). Leaf size: 68
DSolve[{u''[t]+125/1000*u'[t]+4*u[t] ==3*Cos[t/4],{u[0]==0,u'[0]==0}},u[t],t,IncludeSingularSolutions -> True]
\begin{align*} u(t)\to \frac {32 \left (1023 \left (\sin \left (\frac {t}{4}\right )+126 \cos \left (\frac {t}{4}\right )\right )-2 e^{-t/16} \left (65 \sqrt {1023} \sin \left (\frac {\sqrt {1023} t}{16}\right )+64449 \cos \left (\frac {\sqrt {1023} t}{16}\right )\right )\right )}{5414057} \\ \end{align*}