18.2.5 problem Problem 15.5(a)

Internal problem ID [3488]
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)
Date solved : Monday, January 27, 2025 at 07:39:31 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} f^{\prime \prime }+8 f^{\prime }+12 f&=12 \,{\mathrm e}^{-4 t} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.016 (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)
 

\[ f = \frac {3 \,{\mathrm e}^{-2 t}}{2}+\frac {3 \,{\mathrm e}^{-6 t}}{2}-3 \,{\mathrm e}^{-4 t} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 23

DSolve[{D[ f[t],{t,2}]+8*D[ f[t],t]+12*f[t]==12*Exp[-4*t],{f[0]==0,Derivative[1][f][0]==0}},f[t],t,IncludeSingularSolutions -> True]
 

\[ f(t)\to \frac {3}{2} e^{-6 t} \left (e^{2 t}-1\right )^2 \]