= Consider the differential equation given by: t dt -3y + 18- (A) What is the equilibrium solution? (B) For what value(s) of y will the rate of change be negative? (C) For what value(s) of y will the solution curves be increasing? (D) Draw a grid for the solution curves y vs. t. Place the equilibrium solutions on the grid. Sketch a few solution curves based on your analysis for parts (b) and (c). (E) What is the form of the general solution to this differential equation?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Please answer D and E.

Consider the differential equation given by:
dy
dt
= -3y + 18
(A) What is the equilibrium solution?
(B) For what value(s) of y will the rate of change be negative?
(C) For what value(s) of y will the solution curves be increasing?
(D) Draw a grid for the solution curves y vs. t. Place the
equilibrium solutions on the grid. Sketch a few solution curves
based on your analysis for parts (b) and (c).
(E) What is the form of the general solution to this differential
equation?
Transcribed Image Text:Consider the differential equation given by: dy dt = -3y + 18 (A) What is the equilibrium solution? (B) For what value(s) of y will the rate of change be negative? (C) For what value(s) of y will the solution curves be increasing? (D) Draw a grid for the solution curves y vs. t. Place the equilibrium solutions on the grid. Sketch a few solution curves based on your analysis for parts (b) and (c). (E) What is the form of the general solution to this differential equation?
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