20.21.18 problem Problem 18

Internal problem ID [3945]
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 18
Date solved : Monday, January 27, 2025 at 08:04:51 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 2.724 (sec). Leaf size: 17

dsolve([diff(y(t),t$2)-y(t)=6*cos(t),y(0) = 0, D(y)(0) = 4],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 26

DSolve[{D[y[t],{t,2}]-y[t]==6*Cos[t],{y[0]==0,Derivative[1][y][0] ==4}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{2} \left (-e^{-t}+7 e^t-6 \cos (t)\right ) \]