> restart; > with(plots): > de:=a*diff(y(x),x,x)=sqrt(1+diff(y(x),x)^2); > sol1:=dsolve(de,y(x)); > sol2:=subs(_C1=c1,_C2=c2,remove(has,{sol1},I)[]); > eq1:=subs(x=0,y(0)=0,sol2); > Cat_Cur:=simplify(subs(c2=solve(eq1,c2),sol2)); > restart; > L:=1: x2:=0.3: y2:=0.8: > Length := L = a*(sinh((x2+c1)/a)-sinh(c1/a)): > Cat_Cur := y2 = a*(cosh((x2+c1)/a)-cosh(c1/a)): > fsolve({Length,Cat_Cur},{a,c1}); > fsolve({Length,Cat_Cur},{a,c1},{a=0..1}); > Order := 6: > nullst := solve(series(sinh(z),z) = c*z, z); > z := convert(nullst[2],polynom); > f := t-> arcsinh(c*t); > fs := D(f); > K := simplify(fs(z)); > series(K,c=1);