Solution Found!
In the calculus of plane curves, one learns that the
Chapter 1, Problem 72P(choose chapter or problem)
In the calculus of plane curves, one learns that the curvature k of the curve y = y(x) at the point (x, y) is given by
and that the curvature of a circle of radius r is k = 1/r. Conversely substitutes k = 1/r above to derive a general solution of the second-order differential equation
(with r constant) in the form
.
Thus a circle of radius r (or a part thereof) is the only plane curve with constant curvature 1/r.
Questions & Answers
QUESTION:
In the calculus of plane curves, one learns that the curvature k of the curve y = y(x) at the point (x, y) is given by
and that the curvature of a circle of radius r is k = 1/r. Conversely substitutes k = 1/r above to derive a general solution of the second-order differential equation
(with r constant) in the form
.
Thus a circle of radius r (or a part thereof) is the only plane curve with constant curvature 1/r.
ANSWER:Solution
Step 1 of 2:
In this problem we have to write general solution of the second order differential equation
in the form