Internal problem ID [1734]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2.1, Complex roots. Page 141
Problem number: 6.
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) = 0, y^{\prime }\relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 13
dsolve([diff(y(t),t$2)+2*diff(y(t),t)+5*y(t)=0,y(0) = 0, D(y)(0) = 2],y(t), singsol=all)
\[ y \relax (t ) = {\mathrm e}^{-t} \sin \left (2 t \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 15
DSolve[{y''[t]+2*y'[t]+5*y[t]==0,{y[0]==0,y'[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-t} \sin (2 t) \\ \end{align*}