Internal problem ID [1729]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2.1, Complex roots. Page 141
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 31
dsolve(diff(y(t),t$2)+diff(y(t),t)+y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} {\mathrm e}^{-\frac {t}{2}} \sin \left (\frac {\sqrt {3}\, t}{2}\right )+c_{2} {\mathrm e}^{-\frac {t}{2}} \cos \left (\frac {\sqrt {3}\, t}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 42
DSolve[y''[t]+y'[t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-t/2} \left (c_2 \cos \left (\frac {\sqrt {3} t}{2}\right )+c_1 \sin \left (\frac {\sqrt {3} t}{2}\right )\right ) \\ \end{align*}