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# Core 3 AQA help?

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1. Looked through various sites for a solution to no avail, i'm stuck on Jan 2010 question 7 part b.

"show that d^2y/dx^2=qy(1+y^2), where q is a number to be determined"

the previous question found that dy/dx= 4(1+tan^2 4x)

any help is greatly appreciated!
2. Differentiate again to get .

Using the product rule:
using the fact that and
3. Chain rule
,
.
If it helps you can do that whole u sub, and find du/dx but I haven't done that here.
[I haven't seen the question and didn't realise that you had to find second derivative in terms of y but I hope this helps anyway.]

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