I've been trying to solve a system of differential equations on Mathematica, and I wanted to know why this implementation does not work:
f[t_]:= {x[t],y[t],z[t]}
v[t_]:= f'[t]
A = {a,b,c}
DSolve[{f''[t]==k Cross[v[t],A],f[0]=={0,0,0},f,t]
If I write the system explicitly, on the other hand, it works; why is that? By explicitly I mean:
DSolve[{x''[t] == k(c y'[t]-b z'[t]), y''[t]==k( -c x'[t] + a z'[t]), z''[t]==k( b x'[t]- a y'[t])},{x,y,z},t]
And in this case I'm not able to input an initial value, thus ending up with a whole lot of costants which I don't really care about right now.
What's the problem?