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How to integrate and plot the graph between z vs x,

lc = 2.7*10^-3; H = Sqrt[8] lc; B0 = 
       (H/lc)^2; \ [Theta]t = Pi/2; \[Theta]b = Pi/2;  at (x=0,z=0)

         x'[z] = (-Cos[\[Theta]t]*
        z + (1 - 
         z) (Cos[\[Theta]b + 
         B0/2 z]))/Sqrt[(1 - (-Cos[\[Theta]t]*
         z + (1 - z)*(Cos[\[Theta]b + B0/2 z]))^2)]

I am trying using DSolve:

      DSolve[{x'[z] == 0, x[0] == 0}, x, z] // Quiet
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I tried my best to decode what you have above as it has syntax error and has mixed text in the code.

DSolve can't solve it

lc = 27/10000;
H  = Sqrt[8]*lc;
B0 = (H/lc)^2;
θt = Pi/2; θb = Pi/2;

(*I am assuming at (x=0,z=0) means initial conditions are zero*)

ic = x[0] == 0;
ode = x'[z] == (-Cos[θt]*z + (1 - z) (Cos[θb + B0/2 z]))/Sqrt[(1 - (-Cos[θt]*z + (1 - z)*(Cos[θb + B0/2 z])))];
DSolve[{ode, ic}, x[z], z]

Mathematica graphics

So you could try Numerical

 sol = NDSolveValue[{ode, ic}, x, {z, 0, Pi}];
 Plot[sol[z], {z, 0, Pi}]

Mathematica graphics

After $z=\pi$ the solution becomes complex.

| improve this answer | |
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  • $\begingroup$ Thanks@Nasser, It is working. $\endgroup$ – Gopal Verma Apr 18 at 6:06

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