Radicals and rational exponents. Simplifying 4^(5/3)

limunom623

limunom623

Answered question

2022-11-17

Radicals and rational exponents. simplifying 4 5 / 3

Answer & Explanation

teleriasacr

teleriasacr

Beginner2022-11-18Added 21 answers

To find out the general solution for
x 2 y + x y + n 2 y = 0
we propose a solution with the structure
y = c x λ
After substitution we get at
( λ 2 + n 2 ) c x λ = 0
then
λ = ± i n or
y = c 1 x i n + c 2 x - i n but
x = e log x and e i α = cos α + i sin α
so
y = c 1 e i n log x + c 2 e - i n log x and also
y = C 1 cos ( n log x ) + C 2 sin ( n log x ) is the general solution

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