@Torre 

Yes you are right,

now I'm trying GrtensorII for it,

I've installed it in maple12 now there in operators is Rayeqn[v],

But I could not understand how these operators will work??

In previous query I wanted to know solution of expansion,shear and rotation in terms of initial values as a function of affine parameters.

@Preben Alsholm 

great, it worked.

thanks a lot

@Carl Love 

I selected some specific value of L and E also initial condition for

but whatever value I am giving I'm not getting other kinds of orbits, such as scattering and bound orbits.

I plotted like this,

> Sol := dsolve({r(0) = .1, diff(r(phi), phi) = sqrt(1/16-(1/16*(1-2/r(phi)-.1*r(phi)))*(16/r(phi)^2+1))}, r(phi), numeric);
%;
> plots:-changecoords(plots:-odeplot(Sol, [r(phi), phi], phi = 0 .. 2*Pi, scaling = constrained, coords = polar, linestyle = 4, color = blue), polar);

@Carl Love 

I want to have different orbits for eq,

but I am getting only plunging orbits, how to set initial conditions, can you help? (α=0.0005)

@Carl Love 

Is it possible to have multiple plots of above kind?

@Kitonum 

Thank you,

Can you help me further,

How can I plot a polarplot using numeric solution.?

@Mac Dude 

Thanks 4 ur valuable comments,

It will help me for sure,

first I'll look for boundary value problem,

@Mac Dude 

this solution I am getting on solving the deviation equation, which is

diff(eta(tau), tau, tau)+(8*M^2*lambda^2/(4*tau^2*M^2*lambda^2+Q^2)-32*Q^2*M^2*lambda^2/(4*tau^2*M^2*lambda^2+Q^2)^2)*eta(tau) = 0

solution of this equation will tell about deviation vector and tidal forces on neighbouring geodesics, so it should not be complex.

range of parameters is like,

lambda=1,

tau= -infty to +infty

M and Q can be taken as any positive numbers in three conditions as

M>Q, M=Q, M<Q

To have eta real should I take C1, C2 complex?

@Carl Love 

I have checked the imaginary part, it is close to zero.

range of tau is from -infty to +infty,

M>0 (can be taken any positive number upto infty),

Q>0 (can be taken any positive number upto infty),

lambda=1,

solution eta(tau) is geodesic deviation so it should not be imaginary kind of thing, so I'll have totake C1 C2 accordingly.

@ecterrab yes that's right, I'm doing r(phi) everywhere in calculations,

actually I want to reproduce the orbits related to Schwarzschild Bh where I'm getting this equation,

now how can I proceed with this equation to plot the orbits with different values of E and L.

@Carl Love thanks 4 ur valuable comments,

How can I have more than one odeplots in single frame?

also I want to increase the size of text done by "textplot" in usual plots, how can I do this?

@cosmicstring Thanks a lot

@Kitonum thanks a lot, it worked