@Kitonum metriccalculations.mw(10).mw 

@Kitonum  Thanks please simplify the eqn 3 like before of this maple worksheet :

metriccalculaions_new.mw

@Mariusz Iwaniuk  still showing the same problem .How to resolve this issue?

solve(((∂(-    ∇(f) ))/(∂ t)+((DotProduct(v[0],∇(f)))*(1-e(DotProduct(B,Omega))))+(c[s0]^(2)*rho[1])/(rho[0])(1-e(DotProduct(B,Omega)))+e(CrossProduct(∇ (f),B))*Omega-e*(((DotProduct(-∇(f),Omega))*(DotProduct(B,∇))*(-∇f))+e(E)*(1-(DotProduct(B,Omega)))+e^(2)(DotProduct(E,B))*Omega-e*(((CrossProduct(E,Omega))*(∇(-∇f))))),rho[1]);

Can you share your worksheet?

@tomleslie halfsec^h(u).mw In this worksheet I'm not able to plot  y1(u) and v1(u) it's showing for Error, invalid input: RHS expects 1 argument, but received 0 messages.And when I'm trying to solve the 2nd order differential equation of v(u) it's showing this message- Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct.

nw.m.mw This is the worksheet @tomleslie 

@tomleslie  you can assume any value like a=5  and in the region where u>=5 analytic solution sholud  have a solution like the picture shown below : I have to find analytical solution of x(u) in this form you can take any value of a  ;u<=-5,-5<=u<=5,u>=5 nw.m.mw this is the maple worksheet 

@tomleslie thanks it's working

@tomleslie rt.m.mw

@tomleslie  display part is not working in maple  version 12

@tomleslie The worksheet:ode1.mw I want to plot  three funnctins p(u) ,x(u) and x1(u) in the same plot with bc: x(0)=1,D(x)(0)=0,x1(2)=1,D(x1)(2)=0

Btw Thanks odeSys2.mw it's working.

@tomleslie  this is the maple worksheet. simpODE.mw 

Can't able to plot the numerical solution of v(u).Please help

@tomleslie  Thanks a lott 

6coupled.m.mw this is the worksheet