How Do You Solve This Tricky Differential Equation?

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Discussion Overview

The discussion revolves around solving a specific differential equation, d²m/dx² = -3x. Participants explore methods for finding the complete solution, discuss integration techniques, and consider the implications of the given interval for x, which is from 0 to 4.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant clarifies that m is a function of x and its second derivative is -3x, prompting a discussion about the integration process.
  • Another participant suggests that the problem can be approached by integrating the second derivative to find the first derivative and then the original function, proposing a solution structure.
  • A different participant questions the interpretation of the interval from 0 to 4, suggesting it may relate to definite integrals but is uncertain about the specifics.
  • There is a mention of a separable solution approach, indicating that the problem may have multiple methods of resolution.

Areas of Agreement / Disagreement

Participants express varying approaches to solving the differential equation, with no consensus on the best method or the implications of the interval provided. The discussion remains unresolved regarding the complete solution and the role of the interval.

Contextual Notes

Participants have not provided initial conditions, and there is uncertainty about the interpretation of the interval from 0 to 4 in relation to the solution process.

amix
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Hello :smile:

I have a differential equations, which I don't know how to solve. Maybe somebody has a tip or two

The equation is:
d^2 m / d x^2 = -3x
 
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So m is a function of x and its second derivative with respect to x is -3x? What function gives ax when differentiated? And then what function gives THAT function when differentiated? Do you have any initial conditions?
 
Well, I need to find the complete solution. All I know is that I have a function m(x) and that the interval of x is from 0 to 4.
 
what selfadjoint was getting at was that this is a very easy separable solution, though you've not met those words yet perhaps.

suppose y' = 2x, ( ' means diff wrt x)
then

y= x^2+c

suppose z'' = y' in the above,
then z' = x^2+c,

so what is z?
 
I haven't taken diff. eq. in a while, so I might be wrong, but isn't that like saying:

m" = -3x ?

then just integrate: (I'm using | as the symbol for integral)

|(m" dm) = |(-3x dx)
m' = -3/2 x^2 + C

integrate again, gives:
|(m' dm) = | (-3/2 x^2 + C dx)
m = -1/2 x^3 + Cx + D

That's it!

I don't know what the interval from 0 to 4 falls-in though...
 
Well, wouldn't the interval be just a definite integral from 0 to 4? I may be wrong, if I misread your question. [b(]
 

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