- #1
ballajr
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Homework Statement
1) y' + ycos(t) = 0
2) y' - 2yt = 0
3) y'tan(t) + ysec2(t) = 0
4) Let p(x) be an arbitrary polynomial function. Note that the following is a polynomial
solution to y" = p(x) + y:
y = -p - p" - p(4) - p(6) - ... - p(n)
where n is the smallest positive even integer such that p(n+1) is the zero polynomial.
Prove that the following differential equation has a polynomial solution:
y''' = p(x) + 2y
Homework Equations
The Attempt at a Solution
1) First, I tried moving the ycos(t) to the right, but I don't know where to go from there.
y' = ycos(t)
2) I moved 2ty to the right. Integrated it.
y' = 2ty
3) This one is just a beast. I was never good at trigonometry. I moved the ysec^2t over to the right and canceled out the trig functions to get down to this:
y' = ysec(t)
I don't know where to go from here.
4) I don't even know how to go about doing this problem.