Differential Equations

Question

How do we solve the following differential equation?

dr/[ (m/(r^2)) + vcos(theta) ] = r*d(theta)/(-vsin(theta)

Answer 1

denominator of left side is

m/R^2 + v cos T=

(m + v cos T * R^2)/R^2

left side is:

R^2 dR/(m + v cos T * R^2) = r dT / (-v sin T)

R dR/ (m + v cos T * R^2) = dT/ (-v sin T)

R dR/dt = (m + v cos T * R^2)/(-v sin T)

R dR/dt = (-m/v) csc T - cot T * R^2

cotT R^2 + R dr/dt + (m/v) csc T = 0

or

[cotT R^2 + (m/v) csc T ]/-R = dr/dt

=cot T*R - (m/v) csc T / R

you can now use your favorite Runge Kutta method

for this first order ODE