Integrate the equation in the above problem analytically to find the velocity of the rocket as a function of time.

Also write a MATLAB code to integrate the system numerically using the ODE45 solver. Test your solver on the following data.

The total mass of the rocket at the time of launching is \(600 \times 10^{6} \mathrm{~kg}\), of which \(70 \%\) is fuel. The fuel-consumption rate is \(1640 \mathrm{~kg} / \mathrm{s}\). The exit velocity from the nozzle relative to the rocket is \(3300 \mathrm{~m} / \mathrm{s}\).

Neglect air resistance.

Note that the integration should be done only up to the time of complete burning of the fuel. The results are meaningless after this time.