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 1 2 1 2 + + ... 27 81 243 729 2187 65613. Sketch carefully the solution curves with initial points (0, 1), (0, 2), (, 3), (0, 4), and (ID, 5), without solving the equation (5 points): til\" 2 E(FB) 4. Using Moeionrin series, oompute the following (3 pontts): _ sin(x) x 11m 3 xpn x 5. Find the interval of convergence (don't forgot to oheek the endpoints!) of the following power series (5 points): (2x 9)" Z T