6. In this problem we will show how to solve a specific second order differential equation by reducing it to a first order differential equation. Consider the following differential equation (12 - 2t )y"+4(t - 1)y' + 2y - e2t (a) (4 points) Define the function F(t) - (12 - 20 )y' + (21 -2)y. Verify that the differential equation can be rewritten as dt (b) (4 points) Integrate what you obtain in the previous part to get the first order differential equation (12 - 2t )y' + (2t - 2 )y - e2 + C. for some constant C. (e) (5 points) Solve this first order differential equation (Hint: Is this equation exact?) (d) (2 points) What is the unique solution if we furthermore specify the initial conditions y(0) - 1, y'(0) - 1