In this case the equation arises in the study of the shape of the path that a pursuer, traveling at a speed v_2, must take in order to intercept a prey traveling at speed v_1. use the same substitution as in problem 12 and the initial conditions y(1) = 0, y'(1) = 0 to solve the equation. consider the two cases v_1 = v_2 and v_1 v_2. according to stefan's law of radiation, the rate of change of temperature from a body at absolute temperature t is where t_m is the absolute temperature of the surrounding medium. find a solution of this differential equation. it can be shown that w hen t - t_m is small compared to t_m, this particular equation is closely approximated by newton's law of cooling (equation (3), section 3.2). the height h of water that is flowing through an orifice at the bottom of a cylindrical tank is given by