20.21.21 problem Problem 21

Internal problem ID [3948]
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 21
Date solved : Monday, January 27, 2025 at 08:04:53 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=10 \cos \left (t \right ) \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: 2.818 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 26

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

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