10.11.2 problem 29

Internal problem ID [1356]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.7 Mechanical and Electrical Vibrations. page 203
Problem number : 29
Date solved : Monday, January 27, 2025 at 04:52:13 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{4}+2 u&=0 \end{align*}

With initial conditions

\begin{align*} u \left (0\right )&=0\\ u^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 20

dsolve([diff(u(t),t$2)+1/4*diff(u(t),t)+2*u(t) = 0,u(0) = 0, D(u)(0) = 2],u(t), singsol=all)
 

\[ u = \frac {16 \sqrt {127}\, {\mathrm e}^{-\frac {t}{8}} \sin \left (\frac {\sqrt {127}\, t}{8}\right )}{127} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 30

DSolve[{D[u[t],{t,2}]+1/4*D[u[t],t]+2*u[t] ==0,{u[0]==0,Derivative[1][u][0]==2}},u[t],t,IncludeSingularSolutions -> True]
 

\[ u(t)\to \frac {16 e^{-t/8} \sin \left (\frac {\sqrt {127} t}{8}\right )}{\sqrt {127}} \]