Find the general solution of:

Question

anonymous · Answer

Trigonometry or Differential Equations?

anonymous · Answer

$$y'''' +2y'''+3y''+2y'+y = 0$$

anonymous · Answer

So from the characteristic equation I get $$r^4 + 2r^3 + 3r^2 + 2r + 1 = 0$$  My problem is I'm not seeing how to factor this?

anonymous · Answer

Find its characteristics Equation..

anonymous · Answer

Oh, you have started it..

amistre64 · Answer

if it has rational factors, try descartes rule of sign

amistre64 · Answer

it has no rational roots ....

amistre64 · Answer

what methods are you aware of?

anonymous · Answer

For factoring?

amistre64 · Answer

i was thinking for finding solutions to diffy qs ... factoring this by hand i would think is pretty much impossible in a reasonable amount of time

anonymous · Answer

In my class we just started covering nth order linear homogeneous DEQ's

amistre64 · Answer

have you covered an reduction formulas?

anonymous · Answer

Are you sure, your question is absolutely right?

amistre64 · Answer

my best bet would be to try a power series solution, but that might not be so elegant for this setup

anonymous · Answer

No we have not covered those yet... hmm does this help at all i Just noticed there is a hint says this equation is $$(r^2+r+1)^2$$

amistre64 · Answer

let$$y=\sum a_nx^n\
y'=\sum_0 a_n~n~x^{n-1}\
y''=\sum_1 a_n~n(n-1)~x^{n-2}\
y'''=\sum_2 a_n~n(n-1)(n-2)~x^{n-3}\
y''''=\sum_3 a_n~n(n-1)(n-2)(n-3)~x^{n-4}\
$$
substitute, line up your x^k values and adjust your indexes to match; then its just a matter of working out the resulting solutions

amistre64 · Answer

lol, use the hint, by all means :)

amistre64 · Answer

sites going wonky on me ... :(

amistre64 · Answer

r^2 + r + 1 = 0

quad formula

r = [-2 +- sqrt(1-4(1)(1))]/2

r = -1 +- sqrt(-3)/2