Solve the following differential equations: a. xy'=y+xy b. J y' = y' = x+2y+3 2x-y+5 x+2y+3 x+2y+5 y'=. y cos(x+y)+x+y sin(x+y)+ y cos(x+y)+x+y d. 1 + x 1 e. y"- y'+=y=0 (no guess, please show detailed derivations) X f. y"-3y"+3y'-y = 0 g. xy"-4xy'+6y=x (you need the knowledge from Lectures 4 and 5)