Verify that the indicated function in an explicit solution of the given differential equation. Assume an appropriate interval I of definition for the solution. When you Wo Thus, In terms of X,Consider the following differential equation. dy VxY Let /(x, y) = vay. Find the derivative of . Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (1, Y, ] in the region. There is a unique solution in the entire xy-plane. There is a unique solution in any rectangular region where x 3 0 and y 3 0 or x > 0 and y > 0 or x > 0 and y 0. There is a unique solution in the region . S y.The ambient temperature T In (3) In Section 1.3 * T - T or dt de could be a function of time i. Suppose that in an artificially controlled environment, T ($) is periodic with a 24-hour period, as illustrated in the figure below. A 80 - 40 cos 12 12 Noon Midnight Noon Midnight80 - 40 90s 12 Noon Midnight Noon Midnight Devise a mathematical model for the temperature T(c) of a body within this environment. (Use 7 for It).) * T- 80 + 40 cos 12Reproduce the given computer-generated direction field, Then sketch an approximate solution curve that passes through each of the indicated points, () M-2) - 1\f\f(b) (3) = 0 -1 -2 -2 -3 -3 -2 -1 2 3 -3 -2 -1 1 2 3 "A MILE - MATH156 302122, tactic x + webassign.net/web/Student/Assignment.Responses/submit?pos=38dep =29005-426Atags = autosave#question3894265-3 -3 1 =1 1 3 -1 2 -3 -2 2 -3 -2 -1 -3 -3 -22 3 -3 -1 2 -3 -2 -1 "A MILE - MATH156 302172, tactic x + in webassign net/web/Student/Assignment.Responses/submitipos=38dep=29005-426Atags= autosave/question3894265 3 -3 -2 -1 0 1 2 3 O 3 2 -1 0 1 2 3 -2 2 3 2 -1 2(d) (0) = 0 3 -2 -3 O -3 -2 -1 1 2 -3 -3 -1 1 2 3 OLDOH "A MILE . MATH156 302172, walk x + webmsign.net/web/Student/Assignment.Responses/submit?pos=38dep =29005-426brings=autosave/question3894265_3 -3 -2 -1 2 -2 2ferential equation by separ of variables. 1+2Iny-1Solve the in initial-w Tim problem. 319 Give the largest Interval I over which the solution is defined. (Enter your answer using interval notation.) -00.00Solve the given differential equation by finding, as in Example 4 of Section 2.4, an appropriate integrating factor. (14 - 6+0730) dx - 2dy=0 14 3xSolve the given differential equation by using an appropriate substitution. The DE is homogeneous. -2 + In y CSolve the given differential equation by using an appropriate substitution. The DE is a Bernoulli equation. dy my(* - 1) + celArchaeologists used pieces of burned wood, or charcoal, found at the site to date prehistoric paintings and drawings on walls and ceilings of a cave in Laseaux, France. Use the information in Example 3 of Section 3.1 to determine the appropriate age of a piece of burned wood, if it was found that 83%% of the C-14 found in living trees of the same type had decayed. (Round your answer to the nearest hundred years.) 14648.134 Years