Need help with this initial-value problem

Find the solution of the given initial value problem in explicit form.

y' = x(x²+1) / 4y³, y(0) = -1 /√2

According to my textbook, the correct answer is y= -√((x²+1)/2)

Here is what I am doing and hopefully someone can tell me where I'm going wrong. I can see that it is separable, so I separated it and integrating both sides I got y^4=1/4x^4 + 1/2x² + C. Solving for C I got 1/4, however I am not sure that any of this is correct so far. Anyways, I know I'll never get the right answer unless I get the correct implicit solution and the correct value of C, so help me out with those if what I have written is incorrect!