At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
y^4 = 16 126.96.36.199 = 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