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I am trying to solve this:

$I = \int_0^1(x^2-y^2-(y')^2)$ using the euler equation: $\frac{d}{dx}[\frac{\partial F}{\partial y'}]-\frac{\partial F}{\partial y} =0$

and find the function y(x). So, I have:

$\frac{d}{dx}[2y']-2y=0$. How do I deal with the $\frac{d}{dx}$? Re-writing it in some form of partial derivatives?

CINA
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1 Answers1

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Here is how

$$ \frac{d}{dx}[2y']-2y=0 \implies 2y''-2y=0\implies y''(x)-y(x)=0. $$

Now what's left is to solve the last ode.

science
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    Well, I feel silly. I was thinking that an x derivative would interact strangely with y'. Thanks. – CINA Apr 10 '15 at 12:50
  • @CINA: It happens sometimes that we miss things. You have done a good job. Good luck. You are welcome. – science Apr 10 '15 at 12:52