Recently, I have posted many thourough answers (ex. Differential equations and Fourier and Laplace transforms) on math.stackexchange but felt many were ignored or weren't noticed by users. Conversely, some answers produced in other questions by high rep users, that however good, weren't as comple...

I''l use two theorems to prove your point. One is: THEOREM 1: If $y_1$, $y_2$, $y_3$,$\cdots$, $y_k$ are $k$ solutions of the $$\phi(D)y = 0$$ where $\phi(D)$ is a polynomial in $D =\displaystyle \frac{d}{dx}$ then $$y = \sum_{i=i}^k c_i y_i$$ with each $c_i$ constant is a solution. PROOF...