differential equations Math210

Note: please write down the Answer by hand on paper and also write each answer with the number of the questions

(4) For the following differential equation x y" - xy ty =0 do the following: (a) Show that x = 0 is a regular singular point. (b) Find the indicial equation and show that the indicial roots are equal. (5) Determine the singular points of the equation (x2 -3x-21)y"+ (3+ x)y -(x-7)y = 0 and classify each of them as regular singular point or irregular singular point