August 9th, 2011, 04:11 PM  #1 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  A difficult D.E. for highschool. Solve the first order D.E. $\displaystyle y'(x)=\cos(2x2y)$. Last edited by skipjack; February 18th, 2018 at 12:46 AM. 
August 9th, 2011, 04:32 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,819 Thanks: 2158 
Essentially the same problem appeared in an examination paper over twenty years ago, and the examiners didn't solve it properly!

August 9th, 2011, 04:33 PM  #3 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: A difficult D.E. for highschool. Where and which examination? Last edited by skipjack; February 18th, 2018 at 12:46 AM. 
August 9th, 2011, 04:40 PM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,950 Thanks: 1141 Math Focus: Elementary mathematics and beyond  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!

August 9th, 2011, 04:42 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,819 Thanks: 2158 
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).

August 9th, 2011, 04:48 PM  #6 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  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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