73.19.1 problem 28.6 (a)

Internal problem ID [15599]
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 : 28.6 (a)
Date solved : Tuesday, January 28, 2025 at 08:03:00 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-9 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=9 \end{align*}

✓ Solution by Maple

Time used: 8.533 (sec). Leaf size: 17

dsolve([diff(y(t),t$2)-9*y(t)=0,y(0) = 4, D(y)(0) = 9],y(t), singsol=all)
 

\[ y = \frac {7 \,{\mathrm e}^{3 t}}{2}+\frac {{\mathrm e}^{-3 t}}{2} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 23

DSolve[{D[y[t],{t,2}]-9*y[t]==0,{y[0]==4,Derivative[1][y][0] ==9}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{2} e^{-3 t} \left (7 e^{6 t}+1\right ) \]