18.2.2 problem Problem 15.2(a)

Internal problem ID [3485]
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)
Date solved : Monday, January 27, 2025 at 07:39:18 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} f^{\prime \prime }+2 f^{\prime }+5 f&=0 \end{align*}

With initial conditions

\begin{align*} f \left (0\right )&=1\\ f^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.020 (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)
 

\[ f = \frac {{\mathrm e}^{-t} \left (2 \cos \left (2 t \right )+\sin \left (2 t \right )\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 25

DSolve[{D[ f[t],{t,2}]+2*D[ f[t],t]+5*f[t]==0,{f[0]==1,Derivative[1][f][0]==0}},f[t],t,IncludeSingularSolutions -> True]
 

\[ f(t)\to \frac {1}{2} e^{-t} (\sin (2 t)+2 \cos (2 t)) \]