1. Find the solution of the following equations. For each equation, first, determin the type of the category that the equation belongs to. (a) y' = 1 + y2 xy ( 1 + x2 ) (b) cos 'dx - 2 sin y + cos dy = 0 X X x (c) (2.cy - y)dax + 2xdy = 0 (d) y' + 2y =12 +2.x (e) (xInx - 2xy3 ) dx - 3x2y-dy = 0 (f) da + - + sing) dy = 0 (g) (x + sin x + siny ) da + cos ydy = 0 2. Show that y1 = - and y2 = x are the solutions of y" + -y' 724 = 0. 3. Find the particular solution of y" - 2y' + 10y = 0; y(?) = -1, y'(~) =1. 4. Find the particular solution of 2x y" + 5xy' - 2y = 0; y(1) = 1, y'(1) = 0