Since the independent variable (which I will call "t") does not appear in that equation there is a standard method of reducing the order of the equation (often called "quadrature").

Let y= x'. Then x''= y'= .

So the second order equation for x as a function of t converts to a first order equation for y as a function of x:

(That is the reason for the name "quadrature".)

How difficult those integrals are to do depends strongly on the function f(x).