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I only got to the part:
dy/dt = 2at/3y^2

Just derive again, so you can solve the d^2y/dt^2. :))

it's like solve for y''

let it remain as 3y^2=2at..differntiate again....using multiplication rule....

it says the answer is:
-2a/9y^2
but I am getting a different answer

is "a" here constant?

Quotient rule, remember?

yo constnt

for easier calculation, you can factor out 2a/3 and just derive (t/y^2)

could you show me the first step for the second derivative?
maybe I did something wrong

i'll try again :)

may be u need to substitute y as (at^2)^2/3

I got:
(6ay^4 - 8a^2 t^2 y)/9y^6
I think I am doing something wrong.

i'll try again :)

can you follow @moongazer ?

That's what I got. I think there is some typo in my answer sheet.
Thanks :)

Well you could simplify

@myininaya could you simply it further?
@Yttrium yes, I understood your solution

Could I? Yes. Can you?

Eye ball the numerator and the denominator. You should see they share a common factor.

2a(3y^3 - 4at^2) / 9y^5

that's what I got

You can also choose to write at^2 as y^3

Recall our initial equation: y^3=at^2

I see at^2

Replace it y^3
then combine like terms

@moongazer , do you what myininaya told you?