So I have an integral:(adsbygoogle = window.adsbygoogle || []).push({});

## \delta W=\int_{-\Delta}^\Delta\left[x^2\left(\frac{d\xi}{dx}\right)^2−D_S\xi^2\right]dx ##

Here ##\xi## is a function of ##x## and ##D_S## is a constant. ##\Delta## is just some small ##x##. Now I need to set the variation of ##\delta W## to 0. Do do this I differentiated whatever is inside the bracket and set it to 0. I get:

## x^2\xi″+x\xi′−D_S\xi = 0 ##

However, the answer is:

## \frac{d}{dx}\left(x^2\frac{d\xi}{dx}\right)+D_S\xi = x^2\xi″+2x\xi′+D_S\xi = 0 ##

Where the primes are derivatives with respect to x. As you can see the difference is a factor of 2 in the middle term and that minus sign.

If anyone could point out where I am going wrong, it would be really appreciated.

Thanks!

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# How to set the variation of an integral to 0?

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