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Solving Weissinger's ODE

I can not see why the following does not work as expected,

s = NDSolve[{t * (y[t])^2 * (y'[t])^3 - (y[t])^3 *  (y'[t])^2 +  t * 
(t^2 + 1) * y'[t] - t^2 *y[t] == 0, y[1] == Sqrt[3/2]},   y[t], {t, 1, 10}]

Note, the solution to this nonlinear, non-autonomous, implicit ODE for 
initial condition y[1] = Sqrt[3/2] is just y[t] = Sqrt[t^2 + 1].

Any suggestions on how to obtain the solution (either analytic or 
numerical) would be appreciated.

--V. Stokes

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