73.19.9 problem 28.9 (b)

Internal problem ID [15607]
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 : 28.9 (b)
Date solved : Tuesday, January 28, 2025 at 08:03:05 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+40 y&=122 \,{\mathrm e}^{-3 t} \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 10.153 (sec). Leaf size: 28

dsolve([diff(y(t),t$2)-4*diff(y(t),t)+40*y(t)=122*exp(-3*t),y(0) = 0, D(y)(0) = 8],y(t), singsol=all)
 

\[ y = -2 \,{\mathrm e}^{-3 t} \left (-1+\left (\cos \left (6 t \right )-\frac {3 \sin \left (6 t \right )}{2}\right ) {\mathrm e}^{5 t}\right ) \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 35

DSolve[{D[y[t],{t,2}]-4*D[y[t],t]+40*y[t]==122*Exp[-3*t],{y[0]==0,Derivative[1][y][0] ==8}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-3 t} \left (3 e^{5 t} \sin (6 t)-2 e^{5 t} \cos (6 t)+2\right ) \]