Let $ G $ be a complex linear algebraic group. In other words, $ G $ is a subvariety of the space of $ n \times n $ complex matrices and $ G $ is a group under matrix multiplication.

Does there always exist a differential equation for which $ G $ is the differential Galois group?

For example, $ \mathrm{SL}(2,\mathbb{C}) $ is the differential Galois group of $ E $ over $ K $ where $ K= \mathbb{C}(t) $ is the field of rational functions and $ E $ is the splitting field of the Airy differential operator $ u''(t)-tu(t) $, the source is theorem 4 of https://pi.math.cornell.edu/~hubbard/diffalg1.pdf

Theorem 3 of the same reference say that the differential Galois group of a linear differential equation is always a linear algebraic group. So I am really asking about the converse of Theorem 3: is every complex linear algebraic group the differential Galois group of some linear differential equation?