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Downtime Math #8

Anonymous Sun 11 Aug 07:20:45 2019 No.10879442 View Reply Original Report

Quoted By: >>10880012 >>10880016 >>10880063 >>10880183

Hi /sci/
This one involves a bit of calculus.
Let me know if there's any confusion regarding the question.
Last post: >>10877793

Anonymous

Anonymous Sun 11 Aug 2019 15:13:08 No.10880012 Report

Quoted By:

>>10879442
Let me guess, the differential equation has undefined values when expressed in the real numbers, but those values can be defined when interpreting the differential equation in the complex numbers.

Anonymous

Anonymous Sun 11 Aug 2019 15:15:02 No.10880016 Report

Quoted By:

>>10879442
That's a really long question.

Anonymous

Anonymous Sun 11 Aug 2019 15:41:37 No.10880051 Report

Quoted By:

I've got to be honest, I have no idea how to approach this but I'm going to lurk for the sake of learning

Anonymous

Anonymous Sun 11 Aug 2019 15:50:11 No.10880063 Report

Quoted By: >>10880087 >>10880125 >>10881895 >>10881900

>>10879442
Ok, never mind, this has nothing to do with complex numbers. When we solve the differential equation, the answer isn’t an elementary function, rather, it is two elementary functions glued together. When x is smaller than b, the 3 constants are a = -0.5, b = 4, and c = 2. However, when x is bigger than b, the constants change to a = 0.5, b = 4, and c = 2 (so f(x) is a parabola where half of it is flipped). So, the integral is 8/3, so the sum is 11.

Anonymous

Anonymous Sun 11 Aug 2019 16:05:34 No.10880087 Report

Quoted By: >>10880090 >>10880096 >>10880153 >>10881895 >>10881900

>>10880063
The solution is piecewise defined but not like that, and OP should have given a condition on b, such as b>0. There are two solutions for the integral equation but they are not glued, they have to have the same value at x=0.
The solution is then -0.5 x(x-4) for x<0 and 2 for x>2, and that integral gives 32/3, hence p+q=35
If that is the case the solution is -0.5()

Anonymous

Anonymous Sun 11 Aug 2019 16:06:50 No.10880090 Report

Quoted By:

>>10880087
Ignore the last sentence, rushed editing

Anonymous

Anonymous Sun 11 Aug 2019 16:09:36 No.10880096 Report

Quoted By:

>>10880087
(continuing)
It cannot be assumed that there are two sets of (a,b,c) constants, and the need for a piecewise function comes from the fact that otherwise the solution is zero.

Anonymous

Anonymous Sun 11 Aug 2019 16:22:51 No.10880125 Report

Quoted By:

>>10880063
Fuck, this problem does require something beyond real numbers because f ‘(x)/sqrt(4 - 2*f(x)) = 1 doesn’t produce consistent results when x is increasing on the real line.

Anonymous

Anonymous Sun 11 Aug 2019 16:39:00 No.10880153 Report

Quoted By:

>>10880087
I messed up my post, but the solution is a parabola with b=2 for x<2 and the constant 2 for x>2. p+q=35, no complex numbers needed

Anonymous

Anonymous Sun 11 Aug 2019 16:53:15 No.10880183 Report

Quoted By:

>>10879442
0 by symmetry

Anonymous

View Same Google iqdb SauceNAO Question8Solution.png, 50KiB, 2185x1508

Anonymous Mon 12 Aug 2019 08:16:11 No.10881895 Report

Quoted By:

>>10880063
Not quite. You might want to review your constants.
>>10880087
This is a perfect, though the condition for b is implied in condition 2). Great job!

This is my solution.

Anonymous

View Same Google iqdb SauceNAO Question8Solution.png, 50KiB, 2185x1508

Anonymous Mon 12 Aug 2019 08:18:35 No.10881900 Report

Quoted By:

>>10880063
Not quite. You might want to review your constants.
>>10880087
This is perfect, though the condition for b is implied in condition 2). Great job!

This is my solution.

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