20.21.20 problem Problem 20

Internal problem ID [3947]
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 20
Date solved : Monday, January 27, 2025 at 08:04:52 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y&=8 \sin \left (t \right )-6 \cos \left (t \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 2.742 (sec). Leaf size: 21

dsolve([diff(y(t),t$2)-y(t)=8*sin(t)-6*cos(t),y(0) = 2, D(y)(0) = -1],y(t), singsol=all)
 

\[ y = -4 \sin \left (t \right )+3 \sinh \left (t \right )-\cosh \left (t \right )+3 \cos \left (t \right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 24

DSolve[{D[y[t],{t,2}]-y[t]==8*Sin[t]-6*Cos[t],{y[0]==2,Derivative[1][y][0] ==-1}},y[t],t,IncludeSingularSolutions -> True]
 

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