Solving an Example Euler Equation Problem | Understanding the Reduction Process

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Homework Statement

This is a problem that the book uses as an example and I've been trying since friday to get the same answer but i have not had any success, i need help :(

Well in this problem, F = y(1+(y')^2)^1/2

Homework Equations

eulers eqn

d/dx(partial(F)/partial(y')) - (partial(F)/partial(y)) = 0

The Attempt at a Solution

i get up to

d/dx[y*y'/(1+(y')^2)^1/2)] - (1+(y')^2)^1/2 = 0

but then the book loses me after doing some kind of reduction without showing the steps in between.


after the reduction, they get: y*y"-((y')^2) -1 = 0

could someone help me out with what they did in between? any help is appreciated

 

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Oh my god i am an idiot, i can't believe it took me this long to figure it out...

Ignore thread =/