I. Problem Solving. Kindly enclose in a box your final answer in its simplest form in the solution paper. Please write clearly and legibly. For your final answers, ANY forms of erasures, tampering, and superimpositions shall NOT be considered. Be mindful of your time. God Bless! A. In each of Problems 1 through 3, verify that each given function is a solution of the differential equation. 1. Verify y = x* is a solution to the differential equation " = xyz. 2. Verify y = 4 cos(2x) + 6 sin(2x) is a solution to y" = -4y. 3. Isy = e-* + 2xe-* a solution to y" + 2y' + y = 0. B. In each of Problems 4 and 5, eliminate the arbitrary constant using the method you're comfortable with 4. y = Ae-3x + Be2x 5. y = CeArcsin x C. In each of Problems 6 through 11, determine what type of differential equation of order one (Variable Separable, Homogenous, Exact or Linear) the following equations is and solve the given equations using the type of differential equation you had given. 6. (xy? + y - x)dx + x(xy + 1)dy = 0, when x = 2,y = 2 7. (16x + 5y)dx + (3x + y)dy = 0, when x = 1,y = -3 8. (y2 + 7xy + 16x2)dx + x2dy = 0, when x = 1,y = 1 9. x(x2 + 1 )y' + 2y = (x2 + 1)3, whenx = 1,y = 1 10. (cos 2y - 3x2y?)dx + (cos 2y - 2x sin 2y - 2x3y)dy = 0 11. (3x2 - 2y? )y' = 2xy, when x = 0,y = -1