# Thread: Separating variables and initial condition?

1. ## Separating variables and initial condition?

I have this question: I'm not sure why the fourth option isn't showing up but hopefully it's not needed. When I separated the variables I got 2x^2=arcsint+C and when I solved for C I got the C=8. Is this right? It gave me option two, but I'm just not sure. :/ Thanks!

2. ## Re: Separating variables and initial condition?

Looks good to me!

3. ## Re: Separating variables and initial condition?

Originally Posted by Jester
Looks good to me!
Wait a second, I think the third option works also though? :/

4. ## Re: Separating variables and initial condition?

The identity you're looking for is $\displaystyle \sin^{-1}t=\frac{\pi}{2}-cos^{-1}t$, not $\displaystyle \sin^{-1}t=cos^{-1}t-\frac{\pi}{2}$. So #3 doesn't work.

- Hollywood