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    Hi, I'm just trying a STEP paper and came across a question that I really want to have a good go at but after staring at for half an hour haven't got a faintest clue where to start..

    please don't give the answer, as I could just look that up, but give me that first little hint as to which direction I should be taking the Q.. thanks!

    spoiler hints are welcome

    Question:

    Show that sin(ksin^{-1}x), where k is a constant, satisfies the differential equation
    (1-x^2)\frac{d^2y}{dx^2}-x\frac{dy}{dx}+k^2y=0


    I doubt you can use the same method of solving second order differentials as taught in FP1, and I've tried differentiating the given function but the inverse sin is making it difficult... am I missing something?

    Appreciate the help
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    It's a reasonably tough question if it's the one I think it is (there are several very similar). You can solve the equation, but you need to make a substitution, and it isn't required for this question.

    Remember this question can use material from any of the pure modules (ie if you don't know how to differentiate inverse sine, you either need to work it out, look it up, or give up on the question.
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    alright thanks, I've gotten past the differentiating inverse sin barrier, so I'll see how it goes.
 
 
 
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Updated: November 12, 2008
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