64.20.4 problem 4

Internal problem ID [13647]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 9, The Laplace transform. Section 9.3, Exercises page 452
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 05:54:18 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 8.394 (sec). Leaf size: 18

dsolve([diff(y(t),t$2)+diff(y(t),t)-12*y(t)=0,y(0) = 4, D(y)(0) = -1],y(t), singsol=all)
 

\[ y = \frac {\left (15 \,{\mathrm e}^{7 t}+13\right ) {\mathrm e}^{-4 t}}{7} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 23

DSolve[{D[y[t],{t,2}]+D[y[t],t]-12*y[t]==0,{y[0]==4,Derivative[1][y][0]==-1}},{y[t]},t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{7} e^{-4 t} \left (15 e^{7 t}+13\right ) \]