20.21.16 problem Problem 16

Internal problem ID [3943]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 10, The Laplace Transform and Some Elementary Applications. Exercises for 10.4. page 689
Problem number : Problem 16
Date solved : Monday, January 27, 2025 at 08:04:49 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 y&=10 \,{\mathrm e}^{-t} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 3.200 (sec). Leaf size: 21

dsolve([diff(y(t),t$2)+4*y(t)=10*exp(-t),y(0) = 4, D(y)(0) = 0],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 23

DSolve[{D[y[t],{t,2}]+4*y[t]==10*Exp[-t],{y[0]==4,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

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