- #1

Lujz_br

- 4

- 0

## Homework Statement

Hello, I solved others but not 6.9:

Find the equation of the path joining the origin O to point P(1,1) in the xy plane that makes the integral ∫(y'

^{2}+yy' + y

^{2}) dx stationary.

∫ from O to P. y' = dy/dx

## Homework Equations

I need use ∂f/∂y = d/dx (∂f/∂y') (euler-lagrange equation) with f = y'

^{2}+yy' + y

^{2}

∂f/∂y = y' + 2y

∂f/∂y' = 2y' + y

and d/dx (∂f/∂y') = 2 y'' + y', go to euler-lagrange equation we get:

y' + 2y = 2 y'' + y'

this is equivalent to:

y'' = y (eq 1)

y = e

^{x}is solution of eq. 1, but it don't fit (0,0) and (1,1)

I see the solution at final of the book: y = senh(x)/senh(1)

Ok, is solution of eq. 1 and fit points (0,0) and (1,1).

**There are any thing more? I feel I don't get good answer without look at the final of the book.**

Thanks! Luiz

Thanks! Luiz