# [✓] Include x in the DE returned by the EulerEquations?

Posted 6 months ago
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 So, I need to find an extremal of a given functional J=Integrate[12*x*y+(y')^2,{x,1,3}] To do that I write the Euler's equation and get the DE: 12xy-2*y"=0. Then I try to do the same thing using Mathematica and EulerEquations[] function. And it returns just -2y"=0, ignoring 12x. What am I doing wrong? How to make Mathematica consider the independent variable?
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Posted 6 months ago
 Syntax !!!  Needs["VariationalMethods"]; sol = EulerEquations[12*x*y[x] + y'[x]^2, y[x], x] (* 12 x - 2 (y^′′)[x] == 0 *) First@DSolve[sol, y[x], x] (* {y[x] -> x^3 + C[1] + x C[2]} *) First@DSolve[{sol, y[1] == 0, y[3] == 26}, y[x], x] (* {y[x] -> -1 + x^3} *) 
Posted 6 months ago
 Oh my god, thank you so much! That solved my problem. But what does "First@" do? I couldn't find it in the documentation...
 Delete **First@** you will see the differences. @ is Map function and First is equivalent to FlattenExecute:  ?First or  ??First `