2. Consider the initial value problem. dy -(r – 2)(y – 1)? , y(0) = dx (a) Find any equilibrium solutions of the differential equation. (b) Find an explicit expression for the general solution of the differential equation. (c) Find an explicit expression for the solution of the initial value problem. (d) Use the differential equation to determine where the slope of the family of curves correspond- ing to the general solution is zero, positive and negative. (e) Find the vertical and horizontal asymptotes of the family of curves corresponding to the general solution. (f) Sketch the members of the family of curves corresponding to two values of the arbitrary constant in your general solution. Include and identify in your sketch the curve corresponding to the solution of part (c). Also include and identify any equilibrium solutions you found in part (a).
2. Consider the initial value problem. dy -(r – 2)(y – 1)? , y(0) = dx (a) Find any equilibrium solutions of the differential equation. (b) Find an explicit expression for the general solution of the differential equation. (c) Find an explicit expression for the solution of the initial value problem. (d) Use the differential equation to determine where the slope of the family of curves correspond- ing to the general solution is zero, positive and negative. (e) Find the vertical and horizontal asymptotes of the family of curves corresponding to the general solution. (f) Sketch the members of the family of curves corresponding to two values of the arbitrary constant in your general solution. Include and identify in your sketch the curve corresponding to the solution of part (c). Also include and identify any equilibrium solutions you found in part (a).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please solve the last 3 parts
Transcribed Image Text:2. Consider the initial value problem.
dy
:-(r – 2)(y – 1)2 , y(0) = 0
dx
(a) Find any equilibrium solutions of the differential equation.
(b) Find an explicit expression for the general solution of the differential equation.
(c) Find an explicit expression for the solution of the initial value problem.
(d) Use the differential equation to determine where the slope of the family of curves correspond-
ing to the general solution is zero, positive and negative.
(e) Find the vertical and horizontal asymptotes of the family of curves corresponding to the
general solution.
(f) Sketch the members of the family of curves corresponding to two values of the arbitrary
constant in your general solution. Include and identify in your sketch the curve corresponding
to the solution of part (c). Also include and identify any equilibrium solutions you found in
part (a).
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