Thank you Kay, I'd assume that y[x]^(-1/2) will be automatically sorted out when I run command. I guess that was my mistake.
Also, how do I combine NDSolve and Piecewise together?
For example,
y'[x]==Piecewise[{{x^2 (-1 + y[x])^3 + (3 Sqrt[y[x]])/16 - x^2 (-1 + y[x]) y[x]^3, 0 <= x <=0.5},
{x^2 (-1 + y[x])^3 + (3 Sqrt[y[x]])/16 - x^2 (-1 + y[x]) y[x]^3+30, 0.5 <= x <=1}}]
I tried
NDSolve[{y'[x] ==
Piecewise[{{x^2 (-1 + y[x])^3 + (3 Sqrt[y[x]])/16 -
x^2 (-1 + y[x]) y[x]^3,
0 <= x <= 0.5}, {x^2 (-1 + y[x])^3 + (3 Sqrt[y[x]])/16 -
x^2 (-1 + y[x]) y[x]^3 + 30, 0.5 <= x <= 1}}],
y[0] == 0}, y, {x, 0.000, 1}, Method -> Automatic]
But I get nothing when I plot the graph.