28.3.2 problem 6.37

Internal problem ID [4515]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 6. The Laplace Transform and Its Applications. Problems at page 291
Problem number : 6.37
Date solved : Monday, January 27, 2025 at 09:22:36 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=9 \,{\mathrm e}^{-2 t} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-6 \end{align*}

✓ Solution by Maple

Time used: 2.901 (sec). Leaf size: 18

dsolve([diff(y(t),t$2)+diff(y(t),t)-2*y(t)=9*exp(-2*t),y(0) = 3, D(y)(0) = -6],y(t), singsol=all)
 

\[ y = \left ({\mathrm e}^{3 t}-3 t +2\right ) {\mathrm e}^{-2 t} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 21

DSolve[{D[y[t],{t,2}]+D[y[t],t]-2*y[t]==9*Exp[-2*t],{y[0]==3,Derivative[1][y][0] == -6}},y[t],t,IncludeSingularSolutions -> True]
 

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