Im stuck on Question g).

(3 points) In this question, you will find a Taylor polynomial approximation of degree 4 of the solution to the differential equation: x2)\" 4xy' +6y=0 4 Suppose that we are looking for a solution f (x) = z (1pci = a0 + a1 x + a2x2 + (13 x3 + ax4 to the differential equation. i=1 (a)Whatisao?ao=io i Find f' (x) and f \" (x) and substitute them into the differential equation. (b) Use the fact that two polynomials are equal if and only if they have the same coefficients on like power terms to find the value of al . Then a1 = i 0 (c) Using the same method as in (b) to find the value of ag. What happens when you try to do this? / Any value of a_2 satisfies the equation. vi (d) What is the meaning of your answer to (c)? CA. The Taylor polynomial solution will look like f (x) = a0 + (11 x + 0x2 + (13 x3 + a4x4. (Q B. The Taylor polynomial solution will look like f (x) = a0 + a, x + sz + a3 x3 + tax\" where C is any constant. 0 C. There is no Taylor polynomial solution that will work. (e) Using the same method as in (b) to find the value of a3 . What happens when you try to do this? ' a_3 = D, where D is any constant. V' (f) Using the same method as in (b) to find the value of a4. What happens when you try to do this? ' a_4=0. V' (9) Combine your answers from (a)-(f) to write a polynomial approximation of degree 4 of the solution of the the differential equation. In your answer, you should use C, D, E as the arbitrary constants corresponding to 02 , a3 , 04 respectively. yeil