73.19.3 problem 28.6 (c)

Internal problem ID [15522]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 28. The inverse Laplace transform. Additional Exercises. page 509
Problem number : 28.6 (c)
Date solved : Thursday, March 13, 2025 at 06:10:51 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+8 y^{\prime }+7 y&=165 \,{\mathrm e}^{4 t} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=8\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Maple. Time used: 8.785 (sec). Leaf size: 23

ode:=diff(diff(y(t),t),t)+8*diff(y(t),t)+7*y(t) = 165*exp(4*t); 
ic:=y(0) = 8, D(y)(0) = 1; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = \left (3 \,{\mathrm e}^{11 t}+4 \,{\mathrm e}^{6 t}+1\right ) {\mathrm e}^{-7 t} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 25

ode=D[y[t],{t,2}]+8*D[y[t],t]+7*y[t]==165*Exp[4*t]; 
ic={y[0]==8,Derivative[1][y][0] ==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-7 t}+4 e^{-t}+3 e^{4 t} \]

✓ Sympy. Time used: 0.226 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(7*y(t) - 165*exp(4*t) + 8*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 8, Subs(Derivative(y(t), t), t, 0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 3 e^{4 t} + 4 e^{- t} + e^{- 7 t} \]