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so you never meant to say anything about y right?

Sorry meant r not y.

\[r''=2t^{-3}\]

So we are given r'(1)=1?

Just r(1)=1

dr/dt = t=1?
r'=t=1
I look at that is when t=1 ,r '=1

\[1=\frac{-1}{1^2}+C_1 \]
Solve for C_1

where does the r' come from?

Oh! so another way to look at d^2r/dt^2 is r''?

yep yep

So, since r(1)=1, then t(1)=2, then r of t = 1? Somehow I confused myself...

t(1)=2 makes no sense

I'm sorry to be so blunt

No, it makes no sense to me either.

You are given r'(1)=1 and r(1)=1

|dw:1332451923490:dw|

r'(1)=1 says when t=1 r'=1

\[1=\frac{-1}{1^2}+C_1 \]
The reason why I wrote this

I replaced t with 1 and I replaced r' with 1

Sorry for all these questions...

I don;t understand where you are seeing t(1)=2?