Internal problem ID [837]
Book: Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima,
Meade
Section: Chapter 6.2, The Laplace Transform. Solution of Initial Value Problems. page
255
Problem number: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+5 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 21
dsolve([diff(y(t),t$2)+2*diff(y(t),t)+5*y(t)=0,y(0) = 2, D(y)(0) = -1],y(t), singsol=all)
\[ y \relax (t ) = \frac {{\mathrm e}^{-t} \left (\sin \left (2 t \right )+4 \cos \left (2 t \right )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 25
DSolve[{y''[t]+2*y'[t]+5*y[t]==0,{y[0]==2,y'[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} e^{-t} (\sin (2 t)+4 \cos (2 t)) \\ \end{align*}