Consider the following autonomous first-order differential equation.dy= (y – 2)4dxFind the critical points and phase portrait of the given differential equation.222Classify each critical point as asymptotically stable, unstable, or semi-stable. (List the critical points according to theirstability. Enter your answers as a comma-separated list. If there are no critical points in a certain category, enter NONE.)asymptotically stableunstablesemi-stable

For an autonomous system, dydx=f(y) : The region above or below the equilibrium values on the phase…

Answered: Consider the following autonomous…

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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Answer both questions please
H-11. Is dx = C₁(T)dT + nRT V -dv an exact or inexact differential? The quantity C, (T) is simply an arbitrary function of T. What about dx/T?
dP = 0.9P – 0.0009P2 dt A population is modeled by the differential equation The population is at equilibrium when P = When the population is greater than the equilibrium population, the population is: O decreasing O increasing
2. [15 points] The following differential equation describes the steady-state concentration of a substance that reacts with first-order kinetics in an axially-dispersed plug-flow reactor, as shown in Figure 1: d² c D dx² dc dx U kc = 0, where D = the dispersion coefficient (m2/h), c = concentration (mol/L), U = the velocity (m/h), and k = the reaction rate (1/h). The boundary conditions can be formulated as Ucin = Uc(x = 0) - D dc (x 0) dx dc (x = L) = 0, dx where Cin = the concentration in the inflow (mol/L), and L = the length of the reactor (m). Use the finite-difference method to solve for concentration as a function of distance, given the following parameters: D = 5000 m²/h, U = 100 m/h, k = 2 1/h, L = 100 m, and cin = 100 mol/L. Use centered finite-difference approximations with Ax = 10 m to obtain your solution. Compare your numerical results with the analytical solution: C= Ucin (U — DÀ1)À2e^2ª — (U — DÀ2)À¹³1 × (+20 +212 - 1+1+2) - 4kD ---/ (+1√17) - 10 (1√+420) U 1 = 2D 4kD U…
Construct an autonomous first-order differential equation dy/dx = f(y) whose phase portrait is consistent with the given figure.

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