2.4 problem Problem 15.4

Internal problem ID [2007]

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.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]

Solve \begin {gather*} \boxed {f^{\prime \prime }+6 f^{\prime }+9 f-{\mathrm e}^{-t}=0} \end {gather*} With initial conditions \begin {align*} [f \relax (0) = 0, f^{\prime }\relax (0) = \lambda ] \end {align*}

Solution by Maple

Time used: 0.032 (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)
 

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

Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 28

DSolve[{f''[t]+6*f'[t]+9*f[t]==Exp[-t],{f[0]==0,f'[0]==\[Lambda]}},f[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} f(t)\to \frac {1}{4} e^{-3 t} \left ((4 \lambda -2) t+e^{2 t}-1\right ) \\ \end{align*}