DSolve for system of ODE

Question

i'm having trouble using DSolve for the following equation, which is the position equation of an object moving up a straight hill

My facts are:

g = 9.8
m = 250
u = 0.03
c = 0.74304

And my equation is

DSolve[{ x''[t] == -g*Sin[o]*Cos[o] - (c*x'[t])/m - Cos[o]^2*u*g,
y''[t] == - g + g Cos[o]^2 - (c y'[t])/m-u*g*Sin[o]*Cos[o], 
x[0] == 0, y[0] == 0, x'[0] == v0 Cos[o], y'[0] == v0 Sin[o]}, {x[t], y[t]}, t]

I've been checking, and the Built-in guide is not quite useful since the format it suggests does not work for me, if I don't use the [t] at the end while stating the {x,y},t].

thank you!

Answer 1

Rationalize the parameters

params = Rationalize[{g -> 9.8, m -> 250, u -> 0.03, c -> 0.74304}, 0]

Now you can solve your problem

DSolve[{x''[t] == -g*Sin[o]*Cos[o] - (c*x'[t])/m - Cos[o]^2*u*g, 
   y''[t] == -g + g Cos[o]^2 - (c y'[t])/m - u*g*Sin[o]*Cos[o], 
   x[0] == 0, y[0] == 0, x'[0] == v0 Cos[o], y'[0] == v0 Sin[o]} /. 
  params, {x[t], y[t]}, t]