The question states : A curve of quickest descent in the vertical plane, where $y$ is vertical and $x$ is horizontal, is the solution of the equation:
(a) $y(1+y'^2)=c$
(b)$\sqrt{y^2-c^2-y'}=c$
(c) $y'\sqrt{a^2-x^2}=\sqrt{x}$
(d) $y'\sqrt{a^2-x^2}=a$
I understood by curve of quickest desent they mean brachistochrone curve, which is the cycliod..so we are supposed to check which of the following differential equation gives the cycliod as solution, I think..
But then finding solution of all this diffferentail equation is also not easy..
Is there a better way to deal with this question...
Thanks in advance!!