In each of Problems 1 through 12: (a) Find all the regular singular points of the given differential equation. (b) Determine the indicial equation and the exponents at the singularity for each regular singular point. 1. xy" + 2xy' + 6ely = 0 2. xy" - x ( 2+ x )y + (2+x)y=0 3. x(x - 1 )y" + 6x2 y' + 3y = 0 4. y" + 4xy' + 6y = 0 5. xy' + 3(sinx)y - 2y = 0 6. 2x(x + 2)y" +y' - xy= 0 7. x y' + ; (x + sinx)y+y=0 8. (x +1)2 y" + 3(x2 - 1 )y' + 3y =0 9. x(1- x)y" - (1 + x)y + 2xy = 0 10. (x - 2)2 (x + 2)y" + 2xy' + 3(x -2)y =0 11. (4 - x2 ) y" + 2xy' + 3y = 0 12. x(x + 3)2y" - 2(x + 3)y - xy=0 can you please do #1, #5 and #9