The classical general solution of $y''(x)=0$ is $y(x) = C_1 x + C_2$ with $C_1$ and $C_2$ arbitrary constants.
What is the distributional solution of $y''(x) = 0$?
If the distributional solution is $T$, do we start from $$y'' = T = \sum_{n= 1}^\infty x ^ p \delta^{(q)} = 0 $$ if $p> q$ and integrate $2$ times?