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November 16th, 2010, 05:00 AM   #1
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Iranian college post graduation course entrance exams

Quote:
Originally Posted by skipjack
Using high school calculus, the substitution t ? t/a gives
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January 20th, 2011, 08:18 AM   #2
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Quote:
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36- Which substitution will make the equation y' + p(x)y = q(x)y^4 a linear equation?
Multiplying the equation by -3y^(-4) gives -3y^(-4)y' + -3p(x)y^(-3) = -3q(x), so the substitution z = y^(-3) will produce a linear equation.
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January 24th, 2011, 04:44 AM   #3
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Re: Iranian college post graduation course entrance exams

If you can solve any question, feel free to post your solution. Be aware that these problems are tricky and wrong answers are among choices!!
There might be some translation and or type mistakes, If you have a better translation for some questions, your suggestion is welcome.





This page is available in pgexam.e-rasht.com/civil2010.html
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January 24th, 2011, 05:18 AM   #4
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Re: Iranian college post graduation course entrance exams

44)

Use of partial fraction decomposition gives:





40) We want to find y' in terms of both x and y:



Implicitly differentiate with respect to x:





Multiply through by and solve for y':



The family of orthogonal curves will then satisfy:



Separate variables and integrate:





Multiply through by 2 and rearrange:

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January 24th, 2011, 06:06 AM   #5
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Re: Iranian college post graduation course entrance exams

41)

L'H˘pital's rule

42)

Rewrite as , simplify, and use L'H˘pital's rule.
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January 24th, 2011, 08:16 AM   #6
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Re: Iranian college post graduation course entrance exams

45)









43)
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February 27th, 2011, 03:22 AM   #7
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Re: Iranian college post graduation course entrance exams

The web page containing the questions is removed; I have uploaded them again, sorry for the inconvenience!
Here are the questions:


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