Internal problem ID [2338]
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 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 5, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 17
dsolve([diff(y(t),t$2)+4*y(t)=0,y(0) = 5, D(y)(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = \frac {\sin \left (2 t \right )}{2}+5 \cos \left (2 t \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 17
DSolve[{y''[t]+4*y[t]==0,{y[0]==5,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 5 \cos (2 t)+\sin (t) \cos (t) \\ \end{align*}