Internal problem ID [2866]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = A, y^{\prime }\left (0\right ) = B] \end {align*}
✓ Solution by Maple
Time used: 1.703 (sec). Leaf size: 13
dsolve([diff(y(t),t$2)-y(t)=0,y(0) = A, D(y)(0) = B],y(t), singsol=all)
\[ y \left (t \right ) = A \cosh \left (t \right )+B \sinh \left (t \right ) \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 33
DSolve[{y''[t]-y[t]==0,{y[0]==a,y'[0]==b}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^{-t} \left (a \left (e^{2 t}+1\right )+b \left (e^{2 t}-1\right )\right ) \]