Please leave explanation and what solution did use. This is Linear Differential Equation

Instructions: Solve the following problems. (2 items x 10 points) 1. The machine is defined by the operator 2. The machine is defined by the operator X = 2K2 + D + 3 where Y = 4D(K) + 1 where K: fef K:gg+3x Show the detailed solution of X operating on f Show the detailed solution of Y operating on g to produce X(f). to produce Y(g). f (x) = In(x) g(x) = 2x + 1 Hint: eln(x) = x x(f(x)) = 2e*+=+3In(x) X Y(g(x)) = 2x + 21