MATLAB: How to solve this 2nd order ODE with time-dependent parameters

Question

 2nd ODE to solve
   dx/dt*(a + f(t))* d2x/dt2 + 0.5*b*(dx/dt)^2 + k(t)*(dx/dt)^2 - g(t) = 0
   Boundary condition: dx/dt(0) = v0
 where
   - 't' is the time, 
   - 'x' is the position
   - 'dx/dt' is the velocity
   - 'd2x/dt2' is the acceleration
   - 'a', 'b', 'v0' are constants
   -  'f(t)', 'k(t)' and 'h(t)' are KNOWN functions dependent on 't' 
             (I do now write them because they are quite big)

Since I am new in Matlab, I would like to know how to code this with ode45. Thank you in advance

Answer 1

v0 = ...;
tstart = ...;
tend = ...;
a= ...;
b =...;
fun=@(t,y)(g(t)-(0.5*b+k(t))*y(1)^2)/(y(1)*(a+f(t)));
[T,Y]=ode45(fun,[tstart tend],v0);

Best wishes

Torsten.