Chapter 6.9, Problem 423E

For the following exercises, use this scenario: A cable hanging under its own weight has a slope $S=dy/dx$ that satisfies $dS/dx=c\sqrt{1+S^2}$ . The constant c is the ratio of cable density to tension.

423. Integrate $dy/dx=\sinh \left(cx\right)$ to find the cable height $y\left(x\right)$ if $y\left(0\right)=1/c$ .