Internal problem ID [2357]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = A, y^{\prime }\relax (0) = B] \end {align*}
✓ Solution by Maple
Time used: 0.024 (sec). Leaf size: 23
dsolve([diff(y(t),t$2)-y(t)=0,y(0) = A, D(y)(0) = B],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (A -B \right ) {\mathrm e}^{-t}}{2}+\frac {{\mathrm e}^{t} \left (B +A \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 14
DSolve[{y''[t]-y[t]==0,{y[0]==a,y'[0]==b}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to a \cosh (t)+b \sinh (t) \\ \end{align*}