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Plotting after integrating the solution of system of differential equations

• To: mathgroup at smc.vnet.net
• Subject: [mg123988] Plotting after integrating the solution of system of differential equations
• From: Itzhak Shechtman <shechtma at netvision.net.il>
• Date: Wed, 4 Jan 2012 05:02:06 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

I would be grateful for any help in overcoming this:

In the system

1.
q[x_,y_]=1+2 x+x^2+y^2;
k[x_,y_]=(4 x/(1+2 x+x^2+y^2))^0.5;
B=5.5 10^7;
sol=NDSolve
[{x''[t]==B*(2(1-k[x[t],y[t]])^2*EllipticK[k[x[t],y[t]]]-(2-k[x[t],y[t]]^2*(1+x[t]))*EllipticE[k[x[t],y[t]]])/(q[x[t],y[t]]^1.5*k[x[t],y[t]]^2*(1-k[x[t],y[t]]^2)),
y''[t]==B*2 y[t]*EllipticE[k[x[t],y[t]]]/(q[x[t],y[t]]^1.5*(1-k[x[t],y[t]]^2)),x[0]==p,x'[0]==0,y[0]==-10^5,y'[0]==v},{x,y},{t,0,20}];

2.
sol1=NIntegrate[y'[20]/.sol,{p,0.01,1}];

3.
Plot[y'[20]/.sol1,{v,10^3,10^5}]

I don't know how to combine the 3 parts of the problem.
Thank you for taking the trouble.   Itzhak Shechtman