## Nada721 2 years ago Find the general solution of the given differential equation 2y''+ 2y'+y = 0 Please help me solve this.

1. modphysnoob

use the characteristic equation, do you know how?

Yes it's just the answer has sine and cosines in it and I don't know how they got it

3. Spacelimbus

that's because your answer are complex conjugated solutions. Have you dealt with them before?

No. All of the other questions were not like that

5. Spacelimbus

It's a bit hard to explain the nature of complex numbers and how they apply to Differential Equations in just one post, it's a rather big topic, but if you want, I can link you to Pauls Website where he deals with complex solutions.

6. modphysnoob

just solve it using characterist equation; you should get expoential(like you always do) but with complex power; use euler idenity to get sin/cos

I was looking at it earlier under repeated roots and reduction order but it didn't help

Euler's identity? Yea we didn't cover that. I guess il try looking that up