Verify that the indicated function y=ϕ(x)y=ϕ(x) is an explicit solution of the given first-order differential
equation. By considering ϕϕ simply as a function, give its domain. Then by considering ϕϕ as a
solution of the differential equation, give at least one interval II of definition.
y′=25+y2;y=5tan5xy ′ =25+y 2 ;y=5tan5x

Along 8-cm diameter steam pipe whose external surface temperature is 900c connects two buildings. the pipe is exposed to ambient air at 70c with a wind speed of 50 km/hr blowing across the pipe. determine the heat loss from the pipe per unit length. (b) air at 500c enters a section of a rectangular duct (15 cm x 20 cm) at an average velocity of 7 m/s. if the walls of the duct are maintained at 100c. a) the length of the tube for an exit temperature of the air to be 40 0c. b)the rate of heat transfer from the air. c) the fan power needed to overcome the pressure drop in this section of the duct.