first order differential equation question

The problem is : dy/dx=(x(x^2+1))/4y^3 when y(0)=-1/√2
This is my work so far:
∫4y^3dy=∫x(x^2+1)dx
(y^4)/2=((x^2+1)^2)/2+c
The answer from the textbook is y=-(√(x^2+2)/2)
As you can see, my work will never equal the textbook answer when you put it in the y= stuff form. What did I do wrong?
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 I got a slightly different answer than what you posted from the text $y(x) = -\sqrt{\frac{1}{2}(x^2+1)}$ and mathematica agrees with me, so perhaps a typo? Anyway, it looks like your on the right track, although go back through the integration, I think you may be off by a factor. Then apply the boundary condition to find the integration constant. And simplify the algebra down to the answer. Also be conscience of taking roots, $y(x) = ±(stuff)^{1/4}$ good luck

 Tags differential eqns