NIntegrate and Plot solution of differ. equa. over initial conditions

*To*: mathgroup at smc.vnet.net*Subject*: [mg124392] NIntegrate and Plot solution of differ. equa. over initial conditions*From*: Itzhak Shechtman <shechtma at netvision.net.il>*Date*: Wed, 18 Jan 2012 05:59:51 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

Hi all, I would be grateful for any help. I have the set of 2 ordinary differential equations: Clear[sol, q, k]; B = 5.5*10^7; q[x_, y_] = 1 + 2 x + x^2 + y^2; k[x_, y_] = 2 (x/(1 + 2 x + x^2 + y^2))^0.5; sol[p_?NumericQ,v_ ?NumericQ]:=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]== v, y[0]==-100000}, {x, y}, {t, 0,2}]; I wish to: 1) sol1=NIntegrate[p*v*(v-y'[2])/.sol,{p,0.1,1}]; and 2) Plot[sol1,{v,10^3,10^5}] Mathematica does not accept it, objecting to solving the equations with non numeric initial conditions( p and v ), despite the above definition of sol. Does anyone have an idea? Thanks for the trouble. Itzhak