Solve the following problems showing any necessary work 1 Co

Solve the following problems, showing any necessary work. 1 Consider the following differential equation. (Do NOT solve it!) {x - 5)i/ - (x2 + 2 )y = cot x, y( 4) = 3 Find the largest interval I containing 4 such that there is a unique solution to this DE which is defined for all x in I. (Do NOT solve this equation!) 2. Consider the linear homogeneous differential equation x2 y\" + 2x y\' - 6 y = 0. a. Find two different solutions y1{x) and y2(x) to this equation, of the form y(x) = xr. b. Calculate and simplify the Wronskian W(y1,y2) of these two solutions. You should end up with an expression which is not always equal to zero. c. Solve the initial value problem x2y\" + 2xy\'-Gy = 0, 2/(1) = 5, y\'(l) = -10. d. Do NOT solve the differential equation in

Solution

No. It is not possible using circles.

Two circles intersect in at maximum 2 points. Each of the intersections will make a new region.

Since the fourth circle intersects the first three in at most 6 places, it creates at most 6 new regions; that\'s 14 total. So there is no possible way that all 16 different regions that arise in the case of 4 sets be shown with a traditional (circular) Venn diagram.