20.21.12 problem Problem 12

Internal problem ID [3939]
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 12
Date solved : Monday, January 27, 2025 at 08:04:47 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=10 \,{\mathrm e}^{-t} \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 2.940 (sec). Leaf size: 19

dsolve([diff(y(t),t$2)+diff(y(t),t)-2*y(t)=10*exp(-t),y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
 

\[ y = 3 \,{\mathrm e}^{-2 t}-3 \cosh \left (t \right )+7 \sinh \left (t \right ) \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 25

DSolve[{D[y[t],{t,2}]+D[y[t],t]-2*y[t]==10*Exp[-t],{y[0]==0,Derivative[1][y][0] ==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-2 t} \left (-5 e^t+2 e^{3 t}+3\right ) \]