Sketch the isoclines for the equations:

(a)

(b)

(c)

dy ( ') - = xy y -2 dx Problem 9. 7 The equations describing the motion of an earth satellite in the orbit plane are d2 r_r(d8) 2 dt2 dt A satellite is nearly in a circular orbit determined by r and ~~ = w. An exactly circular orbit is defined by r = r u = constant, w = W 0 = constant.

Since dr o = 0 and dwa = 0, the first differential equation is elim·inated for dt dt k2 a circulaT orbit. The second equation reduces to r~w; = - 2 . Find a set of pro linear equations that approximately desrribes the diffcn:nces.

Problem