Internal problem ID [2005]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 15, Higher order ordinary differential equations. 15.4 Exercises, page
523
Problem number: Problem 15.2(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {f^{\prime \prime }+2 f^{\prime }+5 f=0} \end {gather*} With initial conditions \begin {align*} [f \relax (0) = 1, f^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve([diff(f(t),t$2)+2*diff(f(t),t)+5*f(t)=0,f(0) = 1, D(f)(0) = 0],f(t), singsol=all)
\[ f \relax (t ) = \frac {{\mathrm e}^{-t} \left (\sin \left (2 t \right )+2 \cos \left (2 t \right )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 25
DSolve[{f''[t]+2*f'[t]+5*f[t]==0,{f[0]==1,f'[0]==0}},f[t],t,IncludeSingularSolutions -> True]
\begin{align*} f(t)\to \frac {1}{2} e^{-t} (\sin (2 t)+2 \cos (2 t)) \\ \end{align*}