73.18.5 problem 27.1 (e)

Internal problem ID [15589]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 27. Differentiation and the Laplace transform. Additional Exercises. page 496
Problem number : 27.1 (e)
Date solved : Tuesday, January 28, 2025 at 08:02:53 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 y&=20 \,{\mathrm e}^{4 t} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=12 \end{align*}

✓ Solution by Maple

Time used: 9.803 (sec). Leaf size: 21

dsolve([diff(y(t),t$2)+4*y(t)=20*exp(4*t),y(0) = 3, D(y)(0) = 12],y(t), singsol=all)
 

\[ y = 2 \cos \left (2 t \right )+4 \sin \left (2 t \right )+{\mathrm e}^{4 t} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 23

DSolve[{D[y[t],{t,2}]+4*y[t]==20*Exp[4*t],{y[0]==3,Derivative[1][y][0] ==12}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{4 t}+4 \sin (2 t)+2 \cos (2 t) \]