In the given differential equation the point x=0 is a regular singular point. 3x^2 y" + 8xy' + (x - 2)y = 0 a) Show that when using method of Frobenius the solutions of the indicial equation DO NOT differ by an integer. b) Use the method of Frobenius to find two linearly independent solutions of the given equation (find at least the first three nonzero terms). Form a general solution. MAPLE part c) Use Maple to find "polynomial" approximations for n up to 2, 3 and 5. d) Graph the "polynomial" approximations from part c) on the interval 3 lessthanorequalto x lessthanorequalto 15 when initial values are y(0)=1 and y"(0)=1. Use single graph for all three approximations. Provide observation/explanations. Extra credit Maple Use Maple to find solution of the given equation centered at x=1 and at x=5. Repeat parts c) and d). Which one of all obtained approximations (centered at 0, 1 and 5) of the solutions would be best if we are interested in the solution on the intervals (0, 3) and (-1, 3) ? Explain your answer. In the given differential equation the point x=0 is a regular singular point. 3x^2 y" + 8xy' + (x - 2)y = 0 a) Show that when using method of Frobenius the solutions of the indicial equation DO NOT differ by an integer. b) Use the method of Frobenius to find two linearly independent solutions of the given equation (find at least the first three nonzero terms). Form a general solution. MAPLE part c) Use Maple to find "polynomial" approximations for n up to 2, 3 and 5. d) Graph the "polynomial" approximations from part c) on the interval 3 lessthanorequalto x lessthanorequalto 15 when initial values are y(0)=1 and y"(0)=1. Use single graph for all three approximations. Provide observation/explanations. Extra credit Maple Use Maple to find solution of the given equation centered at x=1 and at x=5. Repeat parts c) and d). Which one of all obtained approximations (centered at 0, 1 and 5) of the solutions would be best if we are interested in the solution on the intervals (0, 3) and (-1, 3) ? Explain your