Q7 (a) Sketch the phase line for the autonomous differential equation= f(y), where the graph of the dt function f(y) is given below. (b)ldentify the equilibrium points as sinks, sources, or nodes. (c) Sketch a few solutions of the equation with various initial conditions.

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A: Discriminant of PDE of the form A∂2u∂x2+B∂2u∂x∂y+C∂2u∂y2+D∂u∂x+E∂u∂y+Fu=0 is given by  D=B2-4AC…

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A: Given differential equation is: d2xdt2=-5dxdt+4x+5-x2     ......1 For equilibrium point , d2xdt2=0…

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Q: Sketch the phase line for the given differential equation. Identify the equilibrium points as…

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A: Please see the below picture for detailed solution.

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Q: ketch the phase lines for the given differential equation. identify the equilibrium points as sinks,…

A: To identify the equilibrium points as sinks, sources, or nodes and to plot the phase line for the…

Q: Consider the autonomous nonlinear system Ja' = 2xy, y = e" – y?.

A: This question is about application of functional analysis

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A: Stability type of equilibrium at y=3 in this phase line is

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Q: sketch the phase liens for the given differential equation. identify the equilibrium points as…

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