Exercise 2.1a. Sketch (by hand, without using MATLAB) the direction field of the differential equation dy⁄dx= y⁄5for xand yvalues between -5 and 5. (You do not need to include this sketch in your write-up.)b. On your direction field, add a curve (by hand) that approximates the solution passing through the point x = 0, y = 1.c. Now solve the differential equation given in part (a), either working it out by hand or using the dsolve command that we saw in Assignment 1. Compare your answers to parts (a) and (b)

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?