1. Consider the following second-order differential equation. d^2x/dt^2 + 3 dx/dt + 2x − x^2 =...

1. Consider the following second-order differential equation. d^2x/dt^2 + 3 dx/dt + 2x − x^2 = 0 (a) Convert the equation into a first-order system in terms of x and v, where v = dx/dt. (b) Find all of the equilibrium points of the first-order system. (c) Make an accurate sketch of the direction field of the first-order system. (d) Make an accurate sketch of the phase portrait of the first-order system. (e) Briefly describe the behavior of the first-order system

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Expert Solution

For plotting phase potrait, the eigenvector corresponding to the eigenvalue is pointed and then a line is drawn through that point which crosses origin. If the eigenvalue is negative then it goes into the origin. Then, select the most negative eigenvalue and draw a curve parallel to it's line and while it reaches origin, converge it to the origin. This is the phase potrait.

Colby Messinger answered 8 months ago

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