How can I solve this:
$\frac{d^4G}{dx^4} = \delta(x-\bar{x}) $ Boundary conditions: $G(0) = G'(0) = G''(1) = G'''(1) = 0$
I tried:
Let $G(x) = A_1x^3+A_2x^2+A_3x+A_4$ if $ x < \bar{x}$ and $G(x) = B_1x^3+B_2x^2+B_3x+B_4 $ if $x>\bar{x}$
then using the boundary conditions I get all the coefficients are zero, but when I put this in wolframalpha it gives me an answer.
Thanks