Do the following problems showing all your work. Be sure to submit your solutions in PDF format to the Assignment area. (Point values are given in the square brackets.) 1. [3] Find the general solution for the differential equation: 3- + 7- dy - 11y =0 dx 2. [4] Find the solution for the initial value problem: dy d.x2 67 Ay + 9y = 0;y(1) = 1;y'(1) = 1 3. [4] Find the general solution for the differential equation: 4- day dx dy + 26y = 0 4. [4] Find the solution for the initial value problem: day - 2 dx MY+y = oy(0) = 1;y'(0) =-2 5. [4] Find the particular solution for the differential equation: d'y + 27 d.x2 242 + 2y = 4xe-*cos (x) 6. [2] Determine the form of the particular solution for the equation (do not evaluate the coefficients): dy - 12y = 2xbe-3x dx2 dx 7. [4] Find the particular solution (using undetermined coefficients) for the differential equation: - By = sin(x)