Geodetic differential equations

Is there a parametric solution in terms of geodetic length s on the
surface of an ellipsoid of the following differential equations?
So far I have calculated geodesics using finite elements and got
hopefully somewhere near to exact values using a = 3675, b = 6354, and
s in elements of 10

1. dphi/ds = (1/rho) * (cos alpha)
2. dlambda/ds = (1/nu) * (sec phi) * (sin alpha)
3. dalpha/ds = (1/nu) * (tan alpha) * (sin alpha)
Where
lambda = longitude
phi = latitude
a = major semi axis
b = minor semi axis
nu = radius of curvature perpendicular to meridian
rho = radius of curvature of meridian
e = eccentricity
alpha = azimuth of geodesic

And
e^2 = (a^2 - b^2) / a^2
nu = a / (1 - e^2 * (sin phi)^2)^(1/2))
rho = nu*(1 - e^2) / (1 - (e^2) * ( sin phi)^2)

Suggestion:
Use Eulers' Theorem in connection with nu, rho, and alpha

.

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