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y^4 = 16 184.108.40.206 = 4.4 = 16 -2.-2.-2.-2 = 4.4 = 16
O.k I see that, so my answers should be 2, 2, -2, -2 right?
difference of squares
but I also see a difference of squares...
2 or -2 are the answer :)
so there can be a complex solution as well.....
you want to solve for y? or factor it?
all real numbers have 0i as a comlex part
solve for y
since there are no 4rt(...) to worry about, you dont need to include and 0i parts
thing is that I am trying to find the solution to a general differential equation..
y^4 = -16 has complex roots
then you should ask what it is your wanting to figure out lol
+2i and -2i are also the roots.
so the problem is y^4-16y=0
...... maybe :)
at first i just found the +and - 2 as a multiple of four
but then I saw the difference of squares and thought, o.k there are complex numbers so its gonna be different
(2i)^4 = 16.i^2.i^2 = 16 i tend to get lost with that
so i first got y(x)= c1e^(2x)+c2xe^2x+c3x^2e^2x+c4x^3e^2x
what grade are you in
but if i take the complex numbers, then I would get y(x) = c1e^2x + c2e^2x + c3cos 2x + c4sin 2x
Im a sophomore in college.
do you know how to factor a difference of squares?
yeah, I was just wondering if I would to take the Nth root how the question is then I would get +and -2 as a multiple of 4, but at the same time if I do the difference of squares then I will get complex numbers. Ijust want to understand if both answers would be right.
I think since the questions asks to find the general solution to the differential equation, you have to include the complex number as part of your solution
well I will just factor first before I try to solve, that way I can find all the solutions. Thanks for the help though.
you would still get same thing...2, -2, -2i, 2i