20.21.28 problem Problem 28

Internal problem ID [3955]
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 28
Date solved : Monday, January 27, 2025 at 08:04:58 AM
CAS classification : [[_2nd_order, _missing_x]]

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

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 2.560 (sec). Leaf size: 13

dsolve([diff(y(t),t$2)-y(t)=0,y(0) = A, D(y)(0) = B],y(t), singsol=all)
 

\[ y = A \cosh \left (t \right )+B \sinh \left (t \right ) \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 33

DSolve[{D[y[t],{t,2}]-y[t]==0,{y[0]==a,Derivative[1][y][0] ==b}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{2} e^{-t} \left (a \left (e^{2 t}+1\right )+b \left (e^{2 t}-1\right )\right ) \]