How Do You Solve This Tricky Differential Equation?

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SUMMARY

The discussion focuses on solving the differential equation d²m/dx² = -3x, where m is a function of x. The solution involves integrating the equation twice, resulting in m(x) = -1/2 x³ + Cx + D, where C and D are constants of integration. The interval of interest is from 0 to 4, and the solution is confirmed to be a separable solution, allowing for straightforward integration. The participants emphasize the importance of integration techniques in solving second-order differential equations.

PREREQUISITES
  • Understanding of differential equations, specifically second-order equations.
  • Familiarity with integration techniques and constants of integration.
  • Knowledge of the concept of separable solutions in differential equations.
  • Basic calculus skills, including differentiation and integration.
NEXT STEPS
  • Study the method of solving second-order differential equations.
  • Learn about initial value problems and their applications in differential equations.
  • Explore the concept of separable differential equations in more depth.
  • Practice integrating various forms of differential equations to solidify understanding.
USEFUL FOR

Students and professionals in mathematics, physics, and engineering who are dealing with differential equations, particularly those seeking to enhance their problem-solving skills in this area.

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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