Question

y^(6) +y =0
I mean the 6th derivative
Please help

Answer 1

What do you specifically need to find?

Answer 2

the general solution for ODE

Answer 3

I don't know what ODE is, never heard the term before.

Answer 4

characteristics equation for that is \[\lambda ^6 +1=0\]

Answer 5

Nevermind, this is over my head. I haven't taken Calc II, III, or PDE. Good luck.

Answer 6

\[lambda^6 = -1\rightarrow \lambda= \pm i \]3 times, but cannot get the answer.

Answer 7

u need to find 6th roots of \(-1\) but there is a neater way to do this\[\lambda^6+1=0\]\[\lambda^6-i^6=0\]\[(\lambda^3-i^3)(\lambda^3+i^3)=0\]\[(\lambda-i)(\lambda^2+\lambda i-1)(\lambda+i)(\lambda^2-\lambda i-1)=0\]

Answer 8

oh yeah, you are right! but what if I steer in this way
\[-1= e^{i(\pi+2m\pi)}\]

Answer 9

thats very good also...

Answer 10

hey, not good at all. I did and got stuck. hehe. but from yours, how to solve the second and the last one to get lambda?

Answer 11

those are quadratics, use the formula :)

Answer 12

thank you, let me try. however, I still have a question: I know you make 1 = - (-1) = - (i^2) but don't get how to make it = i^6

Answer 13

well \(i^4=1\) u can put \(i^4\) there

Answer 14

ok, i^4*i^2 =i^6= -1?
or i^2 = -1 and (i^2)^3= (-1)^3 = -1? right?

Answer 15

right

Answer 16

bingo, since your smartscore is 99, no need to give you medal , right? just "thanks a ton" XD

Answer 17

:) thats right :D very welcome

Answer 18

hey u made me champion with that medal :D :) :) thanks

Answer 19

hahahaa.... so that means you are champion now? congratulation

Answer 20

lol, yes, thanks

Answer 21

yw