DSolve[{Derivative[2][x][t] == (x[t]*Derivative[1][f][r])/r, Derivative[2][y][t] == (y[t]*Derivative[1][f][r])/r, Derivative[2][z][t] == (z[t]*Derivative[1][f][r])/r},{x[t], y[t], z[t]},t]