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I'm working on the Brachistochrone probem and I've gotten to the equation:

(dy/dx)^2 = (c^2*y)/(1-c^2*y)

the 'hint' given is to use y = sin^2(theta)/c^2 to solve the integral. I haven't done any math for 5 months and i haven't been in a pure math class for over a year, so I'm drawing a complete blank on how to solve this. If someone could point me in the right direction that would help.

Also, I'm having trouble approaching a problem in which I'm asked to find the geodesics on a sphere of unit radius using calculus of variations. I'm asked to express phi as a function of theta but that isn't making sense to me...again, some direction would help me get on track.

(^ is supposed to denote a power)

Thanks

(dy/dx)^2 = (c^2*y)/(1-c^2*y)

the 'hint' given is to use y = sin^2(theta)/c^2 to solve the integral. I haven't done any math for 5 months and i haven't been in a pure math class for over a year, so I'm drawing a complete blank on how to solve this. If someone could point me in the right direction that would help.

Also, I'm having trouble approaching a problem in which I'm asked to find the geodesics on a sphere of unit radius using calculus of variations. I'm asked to express phi as a function of theta but that isn't making sense to me...again, some direction would help me get on track.

(^ is supposed to denote a power)

Thanks

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