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Differential operator

Differential operators can sometimes be treated as ordinary numbers.

 


Explanation

We can write the differential operator with the letter D as

 ,   ,   ,  ... etc.

 


Example 1

In the differential equation

we substitute the differential operator by D2

For (1 + D2)–1 we use the binomium development, that gives

and because Dx5 = 5x4, D2x5 = 20x3, D3x5 = 60x2, D4x5 = 120x, D5x5 = 120, D6x5 = 0, etc. we get

 


Additional information

The Britsch physicist Oliver Heaviside (1850 - 1925) has proposed this technique.

 


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