20.21.14 problem Problem 14

Internal problem ID [3941]
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 14
Date solved : Monday, January 27, 2025 at 08:04:48 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }&=30 \,{\mathrm e}^{-3 t} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 2.621 (sec). Leaf size: 23

dsolve([diff(y(t),t$2)-2*diff(y(t),t)=30*exp(-3*t),y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = \left (3 \,{\mathrm e}^{5 t}-4 \,{\mathrm e}^{3 t}+2\right ) {\mathrm e}^{-3 t} \]

✓ Solution by Mathematica

Time used: 0.081 (sec). Leaf size: 21

DSolve[{D[y[t],{t,2}]-2*D[y[t],t]==30*Exp[-3*t],{y[0]==1,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 2 e^{-3 t}+3 e^{2 t}-4 \]