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August 9th, 2011, 04:11 PM   #1
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A difficult D.E. for highschool.

Solve the first order D.E. $\displaystyle y'(x)=\cos(2x-2y)$.

Last edited by skipjack; February 18th, 2018 at 12:46 AM.
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August 9th, 2011, 04:32 PM   #2
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Essentially the same problem appeared in an examination paper over twenty years ago, and the examiners didn't solve it properly!
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August 9th, 2011, 04:33 PM   #3
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Re: A difficult D.E. for highschool.

Where and which examination?

Last edited by skipjack; February 18th, 2018 at 12:46 AM.
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August 9th, 2011, 04:40 PM   #4
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Re: A difficult D.E. for highschool.

Currently, high schools in Ontario, Canada, don't even come close to this level of calculus. You don't even learn integration!
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August 9th, 2011, 04:42 PM   #5
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One of the UK's biggest examining bodies produces papers that are used mainly in the UK, but also internationally. They used to produce Special papers (popular for those seeking to qualify for "elite" universities such as Oxford and Cambridge), but these were dropped due to lack of demand. This problem (without the 2 factor) appeared on a Pure Mathematics Special paper of around 1989 (not sure of the exact year).
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August 9th, 2011, 04:48 PM   #6
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Re: A difficult D.E. for highschool.

[color=#000000]Thanks skipjack! I think that Oxford university lost its glare the last decade, but Cambridge is at the top. Greg I think that it is better not to learn too much things at highschool and learn them at the university from the beginning, especially if you want to study maths. Many students consume their powers too early! But if you want to enter an institute of technology then you have big gaps if you don't know how to integrate and differentiate, they are not going to teach you fundamental maths there, they expect you to know them. I had many classmates who abandoned their studies because they couldn't get along with maths.[/color]
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