Find constants a and b such that the function y = a sin(x) + b cos(x) satisfies the differential equation y'' + y' − 8y = sin(x).

Dean and karlene get paid to write songs. dean is paid a one-time fee of $20 plus $80 per day. karlene is paid a one-time fee of $25 plus $100 per day. write an expression to represent how much a producer will pay to hire both to work the same number of days on a song.