Internal problem ID [2008]
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 15.5(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {f^{\prime \prime }+8 f^{\prime }+12 f-12 \,{\mathrm e}^{-4 t}=0} \end {gather*} With initial conditions \begin {align*} [f \relax (0) = 0, f^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve([diff(f(t),t$2)+8*diff(f(t),t)+12*f(t)=12*exp(-4*t),f(0) = 0, D(f)(0) = 0],f(t), singsol=all)
\[ f \relax (t ) = \frac {3 \,{\mathrm e}^{-2 t}}{2}+\frac {3 \,{\mathrm e}^{-6 t}}{2}-3 \,{\mathrm e}^{-4 t} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 16
DSolve[{f''[t]+8*f'[t]+12*f[t]==12*Exp[-4*t],{f[0]==0,f'[0]==0}},f[t],t,IncludeSingularSolutions -> True]
\begin{align*} f(t)\to 6 e^{-4 t} \sinh ^2(t) \\ \end{align*}