73.19.3 problem 28.6 (c)

Internal problem ID [15601]
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 : Tuesday, January 28, 2025 at 08:03:02 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*}

✓ Solution by Maple

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

dsolve([diff(y(t),t$2)+8*diff(y(t),t)+7*y(t)=165*exp(4*t),y(0) = 8, D(y)(0) = 1],y(t), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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