Existence, Uniqueness & Bifurcations · Medium problem

Consider the IVP $y' + \dfrac{y}{t + 1} = \sqrt{9 - t}$, $y(0) = 1$. The existence and uniqueness theorem for first-order linear equations guarantees a unique solution on the largest open interval containing $t = 0$ on which the coefficients are continuous. What is the length of that interval?