I have encountered a question that goes like

Octavio Chen

Octavio Chen

Answered question

2022-03-30

I have encountered a question that goes like
ddydx=y3+xcos(x), y(0)=0.
Find the approximate solution which is o(x5)

Answer & Explanation

mhapo933its

mhapo933its

Beginner2022-03-31Added 9 answers

You insert a (truncated) power series up to the 5th order. To determine these coefficients, you need to equate coefficients up to the 4th power in
a1+2a2x+3a3x2+4a4x3+5a5x4+o(x4)
=(a0+a1x++a4x4+o(x4))3+xx32+o(x4).
As everything goes well in this power series expansion, one could also replace o(x4) with the sharper O(x5).

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