How to reduce higher order linear ODE to a system of first order ODE?
Solution 1:
Starting with $$ x^{(n)}=f(t,x,x',x'',\ldots,x^{(n-1)}), $$ you get the system \begin{align*} x_1&=x\\ x_1'&=x'=x_2\\ x_2'&=x''=x_3\\ &\ldots\\ x_{n-1}'&=x^{(n-1)}=x_{n}\\ x_n^{'}&=x^{(n)}=f(t,x_1,x_2,\ldots,x_{n-1}) \end{align*}