Second order constant coefficients (III)

Problem:

2y'' - 3y' + 6y = 0

Solution:

The solutions to the characteristic polynomial are $\frac{3 \pm \sqrt{39}i}{4}$

Skipping all the derivation we have already done in the last post, the answer is

$y = Ae^{\frac{3}{4}}\cos\frac{\sqrt{39}}{4}x + Be^{\frac{3}{4}}\sin\frac{\sqrt{39}}{4}x$