73.20.9 problem 29.7 (d)

Internal problem ID [15618]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 29. Convolution. Additional Exercises. page 523
Problem number : 29.7 (d)
Date solved : Tuesday, January 28, 2025 at 08:03:12 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{-3 t} \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 8.810 (sec). Leaf size: 23

dsolve([diff(y(t),t$2)-6*diff(y(t),t)+9*y(t)=exp(-3*t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = \frac {t \cosh \left (3 t \right )}{6}+\frac {\sinh \left (3 t \right ) \left (-1+3 t \right )}{18} \]

✓ Solution by Mathematica

Time used: 0.069 (sec). Leaf size: 70

DSolve[{D[y[t],{t,2}]-6*D[y[t],t]+9*y[t]==Exp[-3*t],{y[0]==0,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -e^{3 t} \int _1^0-e^{-6 K[1]} K[1]dK[1]+e^{3 t} \int _1^t-e^{-6 K[1]} K[1]dK[1]+\frac {1}{6} e^{-3 t} \left (e^{6 t}-1\right ) t \]