4) Consider the equation (2x? – 3x – 8)y" + 4xy' – y = 0. A solution to this equation is y(x) = > bn (x – 1)" n=0 for some constants b, , E 0,1,2, .. Find the minimum interval of convergence for y(x).

Can you please help me solve this. Specifically questions b and c

Let y"+p(x)y'+q(x)y=g(x) (2)and y'+p(x)y'+q(x)y= 0(3) where p,q and g are continuous on R. Indicate whether the following statements are true or false. Write out the word"true" or“false" in the blank. (a) If p and q are constants, we know how to find the general solution of (2) for any g(x) (b) If and p are constants, we know how to find the general solution of (2) for any q(x) (c) The general solution of (2) is the sum of the general solution of (3) and a particular solution of (2) (d) If y1 and y2 are two solutions of (2), their sum is also a solution of (2) (e) If yland y2 are two solutions of (3), their sum is also a solution of (3) (f) If y1 and y2 are two solutions of (2), their difference is a solution of (3)

11. 2008 BC #92 Let y be the function with first derivative defined by f'(z) = sin) for 0 sx S 2. At what value of x does J attain its maximum value on the closed interval 0 sxS27 (A) 0 (B) 1.162 (C) 1.465 (D) 1.845 (E) 2