76.19.10 problem 10

Internal problem ID [17734]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 5. The Laplace transform. Section 5.4 (Solving differential equations with Laplace transform). Problems at page 327
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 11:01:59 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=18 \,{\mathrm e}^{-t} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=7\\ y^{\prime }\left (0\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 10.257 (sec). Leaf size: 19

dsolve([diff(y(t),t$2)+2*diff(y(t),t)+y(t)=18*exp(-t),y(0) = 7, D(y)(0) = -2],y(t), singsol=all)
 

\[ y = \left (9 t^{2}+5 t +7\right ) {\mathrm e}^{-t} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 21

DSolve[{D[y[t],{t,2}]+2*D[y[t],t]+y[t]==18*Exp[-t],{y[0]==7,Derivative[1][y][0] == -2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t} \left (9 t^2+5 t+7\right ) \]