Internal problem ID [10942]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 5.5 Laplace transform. Homogeneous equations. Problems page 357
Problem number: Problem 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+5 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 13
dsolve([diff(y(t),t$2)+2*diff(y(t),t)+5*y(t)=0,y(0) = 1, D(y)(0) = -1],y(t), singsol=all)
\[ y \left (t \right ) = \cos \left (2 t \right ) {\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 15
DSolve[{y''[t]+2*y'[t]+5*y[t]==0,{y[0]==1,y'[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-t} \cos (2 t) \\ \end{align*}