differential equations – Error on DSolve

I’ve been trying to solve this initial value problem using ‘DSolve()’:

frac{dy}{dt}=1+tspace sin(tspace y),quad y(0)=0, quad t=(0,2)

ClearAll(y, t)
eq1 := {y'(t) == 1 + t *Sin(t y(t)), y(0) == 0};
DSolve(eq1, y(t), {t, 0, 2})

All I get is the Inverse function error.

    Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. >>

The documentation suggests it has to do with the sine function but I’m not sure how to by-pass it.

Any help would be appreciated.