## Differential Equation ---> Behaviour near these singular points

Problem & Questions:(a) Determine the two singular points x_1 < x_2 of the differential equation(x^2 – 4) y'' + (2 – x) y' + (x^2 + 4x + 4) y = 0(b) Which of the following statements correctly describes the behaviour of the differential equation near the singular point x_1?:A. All non-zero solutions are unbounded near x_1.B. At least one non-zero solution remains bounded near x_1 and at least one solution is unbounded near x_1.C. All solutions remain bounded near x_1.(c) Which of the following statements correctly describes the behaviour of the differential equation near the singular point x_2?:A. All solutions remain bounded near x_2.B. At least one non-zero solution remains bounded near x_2 and at least one solution is unbounded near x_2.C. All non-zero solutions are unbounded near x_2.Answers:(a) x_1 = –2 and x_2 = 2(b) C(c) BI understand how to get x_1 and x_2 (by dividing both sides of the differential equation by the function of x in front of the second order derivative), but could someone please tell me why the multiple-choice parts are C and B, respectively? I don't get the reasoning/logic behind why those are the correct answers.Any input would be GREATLY appreciated!