46.6.3 problem 3

Internal problem ID [7349]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 6. Laplace Transforms. Problem set 6.2, page 216
Problem number : 3
Date solved : Monday, January 27, 2025 at 02:50:51 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=11\\ y^{\prime }\left (0\right )&=28 \end{align*}

✓ Solution by Maple

Time used: 0.226 (sec). Leaf size: 17

dsolve([diff(y(t),t$2)-diff(y(t),t)-6*y(t)=0,y(0) = 11, D(y)(0) = 28],y(t), singsol=all)
 

\[ y = \left (10 \,{\mathrm e}^{5 t}+1\right ) {\mathrm e}^{-2 t} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 18

DSolve[{D[y[t],{t,2}]-D[y[t],t]-6*y[t]==0,{y[0]==11,Derivative[1][y][0] ==28}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-2 t}+10 e^{3 t} \]