Science:Math Exam Resources/Courses/MATH103/April 2017/Question 08 (b)
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Question 08 (b) 

Suppose the Taylor series solves the differential equation with the initial condition . (b) Find the recursive relation for . 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

To find the recursive relation, collect all like terms after expressing the differential equation entirely in terms of Taylor series. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Like in part a), write the differential equation
entirely in terms of Taylor series to obtain
Collecting like terms, we obtain
This can be rewritten as
Hence, for all ,
In other words, the following holds for all ,
