Internal problem ID [1733]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2.1, Complex roots. Page 141
Problem number: 5.
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 }+2 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.035 (sec). Leaf size: 32
dsolve([diff(y(t),t$2)+diff(y(t),t)+2*y(t)=0,y(0) = 1, D(y)(0) = 2],y(t), singsol=all)
\[ y \relax (t ) = \frac {{\mathrm e}^{-\frac {t}{2}} \left (5 \sqrt {7}\, \sin \left (\frac {\sqrt {7}\, t}{2}\right )+7 \cos \left (\frac {\sqrt {7}\, t}{2}\right )\right )}{7} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 48
DSolve[{2*y''[t]+3*y'[t]+4*y[t]==0,{y[0]==1,y'[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{23} e^{-3 t/4} \left (11 \sqrt {23} \sin \left (\frac {\sqrt {23} t}{4}\right )+23 \cos \left (\frac {\sqrt {23} t}{4}\right )\right ) \\ \end{align*}