73.19.10 problem 28.9 (c)

Internal problem ID [15608]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 28. The inverse Laplace transform. Additional Exercises. page 509
Problem number : 28.9 (c)
Date solved : Tuesday, January 28, 2025 at 08:03:06 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-9 y&=24 \,{\mathrm e}^{-3 t} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 8.637 (sec). Leaf size: 21

dsolve([diff(y(t),t$2)-9*y(t)=24*exp(-3*t),y(0) = 6, D(y)(0) = 2],y(t), singsol=all)
 

\[ y = \left (-4 t +2\right ) {\mathrm e}^{-3 t}+4 \,{\mathrm e}^{3 t} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 23

DSolve[{D[y[t],{t,2}]-9*y[t]==24*Exp[-3*t],{y[0]==6,Derivative[1][y][0] ==2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-3 t} \left (-4 t+4 e^{6 t}+2\right ) \]