Internal problem ID [2847]
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]]
\[ \boxed {y^{\prime \prime }+4 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 5, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (t \right ) = \frac {\sin \left (2 t \right )}{2}+5 \cos \left (2 t \right ) \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 17
DSolve[{y''[t]+4*y[t]==0,{y[0]==5,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 5 \cos (2 t)+\sin (t) \cos (t) \]