Answer to Question #182084 in Differential Equations for Gordian

Question

d²y/dx²+dy/dx+2y=0

Answer 1

$\displaystyle y'' + y' + 2y = 0\\ \textsf{Auxiliary equation is}\\ m^2 + m + 2 = 0\\ m = \frac{-1 \pm i\sqrt{7}}{2}\\ \therefore y = e^{-\frac{x}{2}}\left(A\cos\left(\frac{\sqrt{7}}{2}x\right) + B\sin\left(\frac{\sqrt{7}}{2}x\right)\right)$