- #1

- 986

- 9

**y''+6y'+13y=0**

So far, I have.....

e

^{rt}(r

^{2}+ 6r + 13) = 0

r

^{2}+ 6r + 13 = 0

r

^{2}+ 6r + ___ = -13 + ___

r

^{2}+ 6r + 9 = -13 + 9

(r+3)

^{2}= -4

r = -3 +/- 2i

Then we have a crazy-looking thing after assuming y = C1e

^{(r1)(t)}+ C2e

^{(r2)(t)}

y = e

^{-3t}(C1e

^{(2t)i}+ C2e

^{(-2t)i}

And using Euler's formula and simplifying a little bit

y = e

^{-3t}( C1 ( cos(2t) + i*sin(2t) ) + C2( cos(-2t) i*sin(-2t) ) )

The answer in the back of the book, however, is something that doesn't even involve imaginary numbers.

What am I missing?