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#1 Re: Help Me ! » Integral Question. » 2015-02-20 18:34:49

Math1

Thanks,
Found more information here: YouTube - Integral of exp(-x^2)

#2 Re: Help Me ! » Integral Question. » 2015-02-19 23:35:18

Math1

The imaginary error function described in the link above: Wikipedia - Error function

States:
-------
In mathematics, the error function (also called the Gauss error function) is a special function (non-elementary) of sigmoid shape that occurs in probability, statistics, and partial differential equations describing diffusion.
-------

The equation:


is a parabola (and not sigmoid shape).  This can be seen by inputting e^x^2 into the Math is Fun Plotter.  GeoGebra also plots the equation as a parabola with axis of symmetry (x=0) and vertex (1,1).

#3 Help Me ! » Integral Question. » 2015-02-17 20:42:57

Math1
Replies: 4

Equation:

The derivative using chain rule:





But, how is the integral determined?

#4 Re: Help Me ! » Differential Equation - Is this solution correct? » 2015-02-07 12:24:53

Math1

Revision1:
Step 6: Solve this to find v
Integration by parts






Step 7: Substitute into   
   to find the solution to the original equation




Derivative:


Test:
Let   





#5 Re: Help Me ! » Differential Equation - Is this solution correct? » 2015-02-07 09:29:21

Math1

Thanks,
Found formula: The intergration of exponential functions

Integration by substitution







Put   
   back again

Formula:

#6 Help Me ! » Differential Equation - Is this solution correct? » 2015-02-06 18:14:48

Math1
Replies: 6

Form for first order linear differential equation:


   and   

Step 1: Substitute
   and   


Step 2: Factor the parts involving v

Step 3: Put the v term equal to zero


Step 4: Solve using separation of variables to find u


   Make   





Step 5: Substitute u back into the equation at Step 2

Step 6: Solve this to find v



Integration by parts






Step 7: Substitute into y = uv to find the solution to the original equation

   Make   

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