Calculus III Need answers for 1 & 2

1. Solve the following differential equations, using the method of separation of variables (4 points each): a) y' = 1 -xty-xy [Implicit solution is fine ) ] b) (1 + cos(x) )y' = (1 + e )sin (x) ; y(0) =0 2. Compute the exact sum of the following series (4 points): 1 2 2 DIN 27 81 243 729 2187 6561