A disk is rotating about a vertical axis in a liquid. If the retardation due to friction of the liquid is proportional to the angular velocity, , find after seconds if the initial angular velocity was .
If the disk is rotating very rapidly, the retardation is proportional to . Find after seconds if the initial amgular velocity was .
Source: March, Herman W., and Wolff, Henry C. (1917). Calculus. New York: McGraw-Hill. (Questions 4 & 5, p. 158)