Given a parametric representation of an ellipse:
$$ x = a\cos t \\ y = b\sin t $$
Say I have a known point $P_0$ at $t = t_0$. Given also a known arc length $d$ on the ellipse:
$$ d = \int_{t_0}^{t_1} \sqrt{a^2\sin^2 t + b^2\cos^2t} \ dt $$
Is there a way to calculate what is $t_1$ analytically?