20.21.17 problem Problem 17

Internal problem ID [3944]
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 17
Date solved : Monday, January 27, 2025 at 08:04:50 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=12-6 \,{\mathrm e}^{t} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=-3 \end{align*}

✓ Solution by Maple

Time used: 2.713 (sec). Leaf size: 30

dsolve([diff(y(t),t$2)-diff(y(t),t)-6*y(t)=6*(2-exp(t)),y(0) = 5, D(y)(0) = -3],y(t), singsol=all)
 

\[ y = \frac {\left (8 \,{\mathrm e}^{5 t}+5 \,{\mathrm e}^{3 t}-10 \,{\mathrm e}^{2 t}+22\right ) {\mathrm e}^{-2 t}}{5} \]

✓ Solution by Mathematica

Time used: 0.333 (sec). Leaf size: 28

DSolve[{D[y[t],{t,2}]-D[y[t],t]-6*y[t]==6*(2-Exp[t]),{y[0]==5,Derivative[1][y][0] ==-3}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {22 e^{-2 t}}{5}+e^t+\frac {8 e^{3 t}}{5}-2 \]