Question

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

Answer 1

use the characteristic equation, do you know how?

Answer 2

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

Answer 3

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

Answer 4

No. All of the other questions were not like that

Answer 5

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.

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

Thank you both for your help