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September 20th, 2015, 12:13 PM   #1
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Euler Lagrange formula

I'm having some trouble trying to figure out the Euler's equations for some differential equations, I have the answer but I'm not sure how the professor is getting them. I know you're suppose to use ∂F/∂y-d/dx(∂F/∂y'=0) but I can't get the partial derivatives and such right to match up the answer.

Problems

Answer 1st: y'' +16y = 0 Answer 2nd: 1 +2y''=0
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September 20th, 2015, 12:24 PM   #2
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I figured out the second one:
∂f/∂y = 0
∂f/∂y'=x+2y'
d/dx(∂f/∂y') = 1+2y''

but one the second I'm not quite getting the answer:
∂f/∂y = 2y'-32'
∂f/∂y'= 2y'+2y
d/dx(∂f/∂y') = -2y''-32 = 0

Any ideas?
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