cable hanged up (high h=5,5 m) between 2 masts (distance d=50 m) 0 point x axis: in the middle between the masts. y(0)= h0= 5 m simple ODE: y'' = 1/a*sqrt(1+(y')^2) substitutio: z=y' : z' = 1/a*sqrt(1+z^2) general solution: z=sinh(a*x+c1) integration: y=1/a*cosh(a*x+c1)+c2; solution initial value problem: y(x) = h0 +1/a(cosh(a*x) - 1) a can be resolved (numerical wolfram alpha, fzero or what ever): 1/a*(cosh(a*d/2)-1) + h0 - h = 0 -> 1/a*(cosh(a*25m)-1) -0.5m = 0 -> a=0.00159979.../m y'(-d/2)=-0.040005.. y'(d/2)=0.040005