Find the point of maximal curvature on the curve defined by the differential equation a(dy/y)=dx.?

Answer 1

Integrating boyh members we get a lny = x + c, c the integration constant. Therefore, y = e^((x + c)/a) = k e^(x/a), since e^(c/a) is also a constant (assuming a <>0).

The radius of curvature is given by r = ((1 + (dy/dx)^2)^(3/2))/|d^2y/dx2^|

dy/dx = k/a e^(x/a) d^y/dx^2 = k/a^2 e^(x/a)

Now it requires a lot of algebraic work. You have to determine dr/dx and find out the point at which r is maximnum