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 : Sunday, March 30, 2025 at 11:55:19 AM
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*}

✓ Maple. Time used: 0.092 (sec). Leaf size: 16

ode:=diff(diff(y(t),t),t)+6*diff(y(t),t)+8*y(t) = exp(-3*t)-exp(-5*t); 
ic:=y(0) = 0, D(y)(0) = 0; 
dsolve([ode,ic],y(t),method='laplace');
 

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

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

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

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

✓ Sympy. Time used: 0.400 (sec). Leaf size: 31

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(8*y(t) + 6*Derivative(y(t), t) + Derivative(y(t), (t, 2)) - exp(-3*t) + exp(-5*t),0) 
ics = {y(0): 0, Subs(Derivative(y(t), t), t, 0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

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