This is a differential equation problem, please answer all parts, thank you!! Gi

Question

This is a differential equation problem, please answer all parts, thank you!!

Given the differential equation y'=y-y, A) State two specific characteristics about the nature of the solution behavior based on prior calculus knowledge B) Sketch the direction field for the differential equation in the rectangular portion of the ty-plane defined by -23ts2, -2sys2. Show all supporting work for creating the direction field. C) Demonstrate that the two characteristics you stated in part A match the direction field you sketched in part B. 2.

Explanation / Answer

(A) The solution is the reciprocal of 1 + cet It is decreasing

(B) The vector in the direction field point upward if y (y-1) > 0 and which occur in two cases when both y > 0 and y > 1, that is above the line y=1. Vectors in he direction field also point upward when both y and y-1 are less than 0. that is below the t axis.

(C) The exponential function 1 + c et tends to infinity as t tends to infinity.

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