Find the solution of 4x2y′′−4x2y′+y=0,x> 04x2y″−4x2y′+y=0,x> 0 of the form y1=xr(1+c1x+c2x2+c3x3+⋯)

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

Sarah took the advertising department from her company on a round trip to meet with a potential client. including sarah a total of 11 people took the trip. she was able to purchase coach tickets for $280 and first class tickets for $1280. she used her total budget for airfare for the trip, which was $6080. how many first class tickets did she buy? how many coach tickets did she buy?

Aconstruction worker has rope 9 m long he needs to cut it in pieces that are each 3 /5 m long how many such pieces can he cut without having any rope leftover?