please solve:

HW01: Problem 16 Solve d_33_ ti (it6 with the initial condition $(0) = 0. me) = | HW01: Problem 17 In very cold weather the thickness of ice on a pond increases at a rate inversely proportional to the thickness. If the ice initially is 0.03 inches thick and 3 hours laterit is 0.075 inches thick, how thick will it be in 12 hours? inches HW01: Problem 18 There is a neat trick for solving differential equation of the form dm 3 7:}? i 1 d: (r) where the right side depends only on the ratio of x and t. The trick is to transform it into a separable equation by changing the dependent variable from .731 to 1; via :13\") = y\"). In this problem you can try the trick for yourself and watch a non-separable differential equation magically become separable! Find a solution $(t) of the differential equation , _ 16:2 + 23:2 _ 10m satisfying $(l) : 5i. a:(t) 2 Some hints: - In orderto make the change of variables from m to y, you will have to replace each :1: by ty. and you will also have to replace :c' by something involving y'. To determinethis something. apply % to the transformation equation x 2 g. - Once the transformation is done, you can use separation of variables to solve the differential equation and determine y(t). After this. don't forget to transform back to a:(t}| by again using a: = ty. HW01: Problem 19 A small turkey at room temperature 75 \"F is placed into an oven at 425 "F. If h = 0.39 per hour is the heat loss coefcient for turkey meat. how long should you cook the turkey so that it is uniformly 180 \"F? hours