Internal problem ID [1728]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2.1, Complex roots. Page 141
Problem number: Example 2.
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 }+4 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 31
dsolve([diff(y(t),t$2)+2*diff(y(t),t)+4*y(t)=0,y(0) = 1, D(y)(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = \frac {{\mathrm e}^{-t} \left (2 \sqrt {3}\, \sin \left (\sqrt {3}\, t \right )+3 \cos \left (\sqrt {3}\, t \right )\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 40
DSolve[{y''[t]+2*y'[t]+4*y[t]==0,{y[0]==1,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{3} e^{-t} \left (2 \sqrt {3} \sin \left (\sqrt {3} t\right )+3 \cos \left (\sqrt {3} t\right )\right ) \\ \end{align*}