A. In each of Problems 1 through 10, solve the given equations using exact differential equations. 1. (6x + y? )dx + y(2x - 3y)dy = 0 2. (y2 - 2xy + 6x)dx - (x2 - 2xy + 2)dy = 0, when x = 1,y = 2 3. v(2uv2 - 3)du + (3u2v2 - 3u + 4v)dv = 0, when u = 1, v = 1 4. (1 + yz + xy? ) dx + (x? y + y+ 2xy)dy = 0 5. (w3 + wz2 - z)dw + (23 + w2z - w)dz = 0, when w = 4, z = 2 6. (cosx . cosy - cotx)dx - (sin x . sin y)dy = 0 7. x(3xy - 4y3 + 6)dx + (x3 - 6x2y2 - 1)dy = 0, when x = 2, y = 0 8. 2xydx + (y2 + x? )dy = 0 9. (xy' +y - x)dx + x(xy + 1)dy = 0, when x = 1,y = 1 10. (1 - xy) 2dx + ly2 + x2 (1 - xy)-2]dy = 0, when x = 3, y = 4