[resolved] Differential Equation

[Arrow_Raider]

I have this problem that I have been working at for the past hour and 30 minutes. I kid you not. I have no friends that are math geniuses so this is really the only place I can go to for help. The problem is online and it tells me whether or not it is correct. I have ended up with a solution that I can't see how is incorrect, but it is rejecting it. I would really appreciate it if someone could help me:

I'm supposed to find a solution to the differential equation:

x^2/(y^2-6)^2 * dy/dx = 1/2y

It needs to satisfy the initial condition of y=sqrt(7) at x=-1.


So first, I seperate the variables to get y and dy on one side and x and dx on the other. I obtain the following:

(2y(y^2-6)^-2)dy = (x^2)dx

I then integrate both sides and get:

-1(y^2-6)=x^3/3+C

C is a constant.

After doing that, I put sqrt(7) in for y and -1 in for x and solve for C. I obtain C=-2/3 I then proceed to solve for Y because the function must be in the format as y=(function) when I enter it on the webpage. I get the following when doing this:

sqrt(6-3/(3C+x^3))

I replace C with the value I got above and get:

sqrt(6-3/(-2+x^3))

When I submit this answer, it claims that it is incorrect. I don't nescessarily want you to give me the answer, I'd just like to know where I went wrong.