Internal problem ID [1730]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2.1, Complex roots. Page 141
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime }+3 y^{\prime }+4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 31
dsolve(2*diff(y(t),t$2)+3*diff(y(t),t)+4*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} {\mathrm e}^{-\frac {3 t}{4}} \sin \left (\frac {\sqrt {23}\, t}{4}\right )+c_{2} {\mathrm e}^{-\frac {3 t}{4}} \cos \left (\frac {\sqrt {23}\, t}{4}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 42
DSolve[2*y''[t]+3*y'[t]+4*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-3 t/4} \left (c_2 \cos \left (\frac {\sqrt {23} t}{4}\right )+c_1 \sin \left (\frac {\sqrt {23} t}{4}\right )\right ) \\ \end{align*}