Note: For more on this method read about buler's Equation and problem $4 in section $.4. 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 (t? - 2t)y" +4(t -1jy + 2y=e". (a) (4 points) Define the function F(t) = (t' - 2t)y + (2t - 2)y. Verify that the differential equation can be rewritten as at (b) (4 points) Integrate what you obtain in the previous part to get the first order differential equation (t2 - 2t)y'+ (2t -2)y = me" + 0, for some constant C. (c) (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 3(0) = 1,y'(0) =1? Note: For more on this idea read about exact second order differential equations in problem 41 of section 3.2