3:05 Thu, Nov 3 M I M . 69% 5. (10 points) The given masses m; are located at the given points P; which are placed in the xy-plane. Find the total mass (m), moments My and My with respect to the x- and y-axis, and the center of mass (x, y ) of this system: 8. (12 points) Given: dy m, = 3 kg placed at point Py = (-1, 1), my = 4 kg placed at point P2 = (2, -1), and my = 8 kg placed at point Pa = (3, 2). dx V2 a) Find the general solution to the differential equation: Total mass (m) = moment (M ) = moment (M ) = 8a) b) Find the particular solution at y (0) =2: center of mass (x, y ) = 6. (10 points) Let p(x) = Vx represent the radial density of a disk. Calculate the mass of the disk of radius 4 inches. 8b 9. (12 points) Solve the following initial-value problem by using integrating factors: x?y' + xy = 1, x> 0, y(1)=2 7. (12 points) Find the general solution of the given differential equation: ay = xzy dx 9)