Internal problem ID [2006]
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(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {f^{\prime \prime }+2 f^{\prime }+5 f-{\mathrm e}^{-t} \cos \left (3 t \right )=0} \end {gather*} With initial conditions \begin {align*} [f \relax (0) = 0, f^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.022 (sec). Leaf size: 25
dsolve([diff(f(t),t$2)+2*diff(f(t),t)+5*f(t)=exp(-t)*cos(3*t),f(0) = 0, D(f)(0) = 0],f(t), singsol=all)
\[ f \relax (t ) = -\frac {\left (-2 \left (\cos ^{2}\relax (t )\right )+1+4 \left (\cos ^{3}\relax (t )\right )-3 \cos \relax (t )\right ) {\mathrm e}^{-t}}{5} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 25
DSolve[{f''[t]+2*f'[t]+5*f[t]==Exp[-t]*Cos[3*t],{f[0]==0,f'[0]==0}},f[t],t,IncludeSingularSolutions -> True]
\begin{align*} f(t)\to \frac {1}{5} e^{-t} (\cos (2 t)-\cos (3 t)) \\ \end{align*}