46.7.2 problem 19

Internal problem ID [7363]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 6. Laplace Transforms. Problem set 6.3, page 224
Problem number : 19
Date solved : Monday, January 27, 2025 at 02:51:00 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&={\mathrm e}^{-3 t}-{\mathrm e}^{-5 t} \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.258 (sec). Leaf size: 27

dsolve([diff(y(t),t$2)+6*diff(y(t),t)+8*y(t)=exp(-3*t)-exp(-5*t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.298 (sec). Leaf size: 21

DSolve[{D[y[t],{t,2}]+6*D[y[t],t]+8*y[t]==Exp[-3*t]-Exp[-5*t],{y[0]==0,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{3} e^{-5 t} \left (e^t-1\right )^3 \]