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a simple question about EulerEquations


Hi,

It seems that mathematica gives a different expression for Euler-
Lagrange equation.

Isn't the answer to:

EulerEquations[  f[u'[x],u[x],x] , u[x] , x]

should be:

Derivative[0, 1, 0][f][Derivative[1][u][x], u[x], x] -
  Derivative[1, 0, 1][f][Derivative[1][u][x], u[x], x] ==0

?

The output that I am getting from mathematica is:

Derivative[0, 1, 0][f][Derivative[1][u][x], u[x], x] -
  Derivative[1, 0, 1][f][Derivative[1][u][x], u[x], x] -
     Derivative[1][u][x]*
   Derivative[1, 1, 0][f][Derivative[1][u][x], u[x], x] -
     Derivative[2][u][x]*
   Derivative[2, 0, 0][f][Derivative[1][u][x], u[x], x] == 0


Thank you



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