46.6.12 problem 12

Internal problem ID [7358]
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 : 12
Date solved : Monday, January 27, 2025 at 02:50:57 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (4\right )&=-3\\ y^{\prime }\left (4\right )&=-17 \end{align*}

✓ Solution by Maple

Time used: 0.224 (sec). Leaf size: 21

dsolve([diff(y(t),t$2)-2*diff(y(t),t)-3*y(t)=0,y(4) = -3, D(y)(4) = -17],y(t), singsol=all)
 

\[ y = -5 \,{\mathrm e}^{3 t -12}+2 \,{\mathrm e}^{-t +4} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 24

DSolve[{D[y[t],{t,2}]-2*D[y[t],t]-3*y[t]==0,{y[4]==-3,Derivative[1][y][4]==-17}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 2 e^{4-t}-5 e^{3 (t-4)} \]