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UnkleRhaukus
 one year ago
\[\frac{\mathrm dx}{\mathrm dt} = 4\pi^2x+x^2\]
\[x_0 = \pi^2,\qquad v_0=0\]
UnkleRhaukus
 one year ago
\[\frac{\mathrm dx}{\mathrm dt} = 4\pi^2x+x^2\] \[x_0 = \pi^2,\qquad v_0=0\]

This Question is Closed

Empty
 one year ago
Best ResponseYou've already chosen the best response.2Is \(\pi\) the circle constant?

Empty
 one year ago
Best ResponseYou've already chosen the best response.2I guess it appears to be a separable differential equation, unless there's some trick going on haha. This is kind of odd looking.

Empty
 one year ago
Best ResponseYou've already chosen the best response.2It has a general solution \[x=\frac{4 \pi^2}{e^{4\pi^2 (c+t)}+1}\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0Yeah, but how did you get that, I thought separable as well, but what is the numeric method :O

Empty
 one year ago
Best ResponseYou've already chosen the best response.2I don't know, there are many numerical methods

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.0the questing is asking me to use the leapfrog integration method, but i'm not convinced it is stable

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1@Astrophysics there was an x left over... usually when it's separable it would be in the form of h(y) dy = f(x) dx and then integrate both sides but that's not the case in this equation :/

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0Ah ok, and I see leap frog method, is this a mechanics problem..mhm

Empty
 one year ago
Best ResponseYou've already chosen the best response.2Yeah, that's how I got my answer, partial fractions. This is separable @UsukiDoll

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0Wolfram confirms, I don't really know leapfrog integration very well, this does remind me of a simple harmonic oscillator, @Empty you know how to do it using the method

Empty
 one year ago
Best ResponseYou've already chosen the best response.2Ok but the real question is, "How do I show that leapfrog integration is stable" and that I don't know.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1X( completely missed that... yes it is separable... (after hours...mind can't think). But what is leapfrog integration?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{\mathrm dx}{\mathrm dt} = 4\pi^2x+x^2 \] \[\frac{dx}{4 \pi^2x+x^2} = dt\] \[\frac{dx}{x(4 \pi^2+x)} = dt\] and then partial fractions... (not doing the rest)

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0Lol I don't think he's allowed to use that

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1_ k forget it *tosses it in the trash*

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1was fun when it was legit.

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0Haha have a medal, @Michele_Laino may be able to help you

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.0Catastrophic, error sorrys

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1nah... could be something I haven't done or idk... it's similar to asking me to do a PDE involving Laplace Equation at after 3 am. My brain can't function at this hour..
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