begin{multline}
%begin{center}
dot{x}=x_1 \
dot{x_1}=x_2 \
vdots \
dot{x_n}= -frac{f_0}{f_n}x_1  -frac{f_1}{f_n}x_2- cdots -frac{f_{n-1}}{f_n}x_n
%end{center}
end{multline}

documentclass{article}
usepackage{tabstackengine}
TABstackMath
begin{document}
begin{equation}
setstacktabulargap{0pt}% Horz. gap between columns
setstackgap{L}{1.2baselineskip}% vert gap between rows
TABbinary% apply {} before and after each cell to set proper = spacing
tabularCenterstack{rcl}{
dot{x}&=&x_1 \
dot{x_1}&=&x_2 \
&vdots&}
end{equation}
end{document}

begin{equation}
begin{array}{ccc}
    dot{x} &= & x_{1} \
    dot{x}_{1} &= & x_{2} \
    &vdots&
end{array}
end{equation}

documentclass[12pt]{article}

usepackage{mathtools} % loads amsmath

begin{document}

begin{align*}
dot{x} &= x_1 \
dot{x}_1 & =x_2 \
&vdotswithin{=} \
MTFlushSpaceAbove
dot{x}_n& = -frac{f_0}{f_n} x_1  -frac{f_1}{f_n}x_2- cdots -frac{f_{n-1}}{f_n}x_n
end{align*}

end{document}