18.2.4 problem Problem 15.4

Internal problem ID [3487]
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 15.4
Date solved : Monday, January 27, 2025 at 07:39:29 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} f^{\prime \prime }+6 f^{\prime }+9 f&={\mathrm e}^{-t} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 26

dsolve([diff(f(t),t$2)+6*diff(f(t),t)+9*f(t)=exp(-t),f(0) = 0, D(f)(0) = lambda],f(t), singsol=all)
 

\[ f = \frac {\left (-1+\left (4 \lambda -2\right ) t \right ) {\mathrm e}^{-3 t}}{4}+\frac {{\mathrm e}^{-t}}{4} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 28

DSolve[{D[ f[t],{t,2}]+6*D[ f[t],t]+9*f[t]==Exp[-t],{f[0]==0,Derivative[1][f][0]==\[Lambda]}},f[t],t,IncludeSingularSolutions -> True]
 

\[ f(t)\to \frac {1}{4} e^{-3 t} \left ((4 \lambda -2) t+e^{2 t}-1\right ) \]