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annoying P5 algebra!

been doing this question for 15 miin- to half and hour and its really starting to bug me - help!!!


y=arsinh x, show that

c) (1+x^2)f'''(x)+3x.f''(x)+f'x) = 0 - looks trivial, but its really long and cant get the LHS to equal teh zero after the differentiation and resubbing it:smile:

(1+x^2) [f''(x)]^2 = 1 (this is given so use it:smile:

pk
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RichE
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Phil23
been doing this question for 15 miin- to half and hour and its really starting to bug me - help!!!


y=arsinh x, show that

c) (1+x^2)f'''(x)+3x.f''(x)+f'x) = 0 - looks trivial, but its really long and cant get the LHS to equal teh zero after the differentiation and resubbing it:smile:

(1+x^2) [f''(x)]^2 = 1 (this is given so use it:smile:

pk


I think your hint is wrong - don't you mean

(1+x^2) [f'(x)]^2 = 1

If you differentiate this you get

(1+x^2) 2 f' f'' + 2x (f')^2 = 0

Divide by 2 f' =/= 0 to get

(1+x^2) f'' + x f' = 0

The differentiate this to get

(1+x^2) f''' + 2x f'' + x f'' + f' = 0

which is what you want

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