Non trivial zeros of the Zeta function using the differential equations

Using the differential equations, we obtain a more flexible expression for the Riemann Zeta function on the right half-plan except the point $s=1$. Thanks to the Riemann functional equation, we obtain an approach to prove that the Zeta function does not vanish at any point $s$ of the critical strip such that $1-2\Re(s)\neq 0$.