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For the differential equation (dy/dx =y^2-5y+6 (a) find the critical points. (b) sketch typical solutions between the equilibrium solutions. (c) classify each critical point as asymptotically stable, unstable or semistable. (d) find lim h(x ), where h, is a solution of the equation for which h(0) = 1.             x->infinity

For the differential equation (dy/dx =y^2-5y+6 (a) find the critical points. (b) sketch typical solutions between the equilibrium solutions. (c) classify each critical point as asymptotically stable, unstable or semistable. (d) find lim h(x ), where h, is a solution of the equation for which h(0) = 1.             x->infinity

Advanced Engineering Mathematics
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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For the differential equation (dy/dx =y^2-5y+6


(a) find the critical points.
(b) sketch typical solutions between the equilibrium solutions.
(c) classify each critical point as asymptotically stable, unstable or semistable.
(d) find lim h(x ), where h, is a solution of the equation for which h(0) = 1.
            x->infinity

dy For the differential equation - у? - 5у +6 dx (a) find the critical points. (b) sketch typical solutions between the equilibrium solutions. (c) classify each critical point as asymptotically stable, unstable or semistable (d) find lim h(x), where h is a solution of the equation for which h(0) = 1. X00
Transcribed Image Text:dy For the differential equation - у? - 5у +6 dx (a) find the critical points. (b) sketch typical solutions between the equilibrium solutions. (c) classify each critical point as asymptotically stable, unstable or semistable (d) find lim h(x), where h is a solution of the equation for which h(0) = 1. X00
Expert Solution
Step 1

(a) To find critical points, we equate dy/dx to zero, hence critical points are given by

dydx=y2-5y+6=0⇒(y-3)(y-2)=0⇒y=3,2

Hence critical points are given by y=2, y=3.

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