can you help me with this one? thanks

1. For each of the following DEs identify if they are: linear and separable, linear but non-separable, non-linear but separable, or non-linear and non-separable. (a) x'(t) = sin(x) cos2(t) (b) y'(x) = ry (1- y (c ) dy M -+3 dt = y cos(t) dt y (d) dy dx = V2y - x (e) y'(x) - sin(x) y = 0 (f) y2(1 - x2)1/2dy - arcsin x dx = 0 For parts (b) and (d), what does the E/U theorem predicts about the solutions of these DEs subject to the IC y(0) = 0