20.21.8 problem Problem 8

Internal problem ID [3935]
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 8
Date solved : Monday, January 27, 2025 at 08:04:44 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 2.621 (sec). Leaf size: 17

dsolve([diff(y(t),t$2)+diff(y(t),t)-2*y(t)=0,y(0) = 1, D(y)(0) = 4],y(t), singsol=all)
 

\[ y = \left (2 \,{\mathrm e}^{3 t}-1\right ) {\mathrm e}^{-2 t} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 18

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

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