Solution to Problem #62

Ignacio Larrosa Cañestro of A Coruña (Spain), Sean James Kelly of Reed College, Paul Lee of Moreno Valley CA, Vivek Kumar Mehra of Mumbai (India), Randall Rathbun, Paul Botham of Ipswich (UK), Mason Smith of Gary IN, Greg McNulty of Los Angeles CA, Peter Zurej of Celje (Slovenia), Gunnar Þór Magnússon, a student at Flensborg College (Iceland), Ross Millikan of San Mateo CA, Matt Hudelson of Washington State University, Jan van Delden of Zuidhorn (Netherlands), Marcello Cammarata of Cassina de' Pecchi (Italy), Robin Stokes of the University of New England (Australia), and Rob Johnson of West Hills CA solved the problem. Here is Ross Millikan's solution:

We require that Integral(ydx) = Integral(sqrt(1+y'2)dx) over any
interval.

As the interval is arbitrary, the integrands must be equal

So y = sqrt(1 + y'2)

dy/sqrt(y^2-1) = dx

Integrating

Arc cosh(y)=x+c

y=Cosh(x+c)

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