Challenging Algebra + a little bit of Integration Question (1 Viewer)

[dan964]

Have a try using BOS approved calculators only (no Wolfram Alpha)

 

[KingOfActing]

Is that s supposed to be s or y?

 

[seanieg89]

This is just quite tedious, not challenging.

 

[He-Mann]

At least provide links to definitions of terms and notations used in the question most highschoolers wouldn't know.

 

[KingOfActing]

I can see how to do it, but I don't see how the first part relates to the second --- just a bunch of fractions and expanding binominals

 

[InteGrand]

I can see how to do it, but I don't see how the first part relates to the second --- just a bunch of fractions and expanding binominals

Which first part? He probably provided the differential equation to give a taste of Picard iteration. (But yeah, don't need it for the actual question.)

 

[seanieg89]

At least provide links to definitions of terms and notations used in the question most highschoolers wouldn't know.

You could ignore most of the text in the question. All that matters is the recurrence:



The question is literally just to compute which amounts to expanding large polynomials and integrating. f_3 is something like a degree 13 polynomial with massive coefficients. Do it if you feel like grinding out some hand calculations but don't expect any pretty math.

Aside:
Why these things are useful is this iterative procedure lets us prove that solutions to certain differential equations exist / find good approximations to them. For large n, f_n is a good approximation to the solution of the differential equation:

y'(x)=y(x)^3+y(x)^2+y(x)
y(0)=1.