Given the system of nonlinear DEs r' = -2x – 3y + xe and y' = 3.x – y+2 – 2e: (a) Linearise the system of DEs at the critical point (0,0). (b) Using (a), analyse the critical point (0,0). What type of point is it? Is it stable?

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A: dxdt=3x+2y-y2=f(x,y)dydt=-2x-2y+xy=g(x,y)Now, put f(x,y)=0 and g(x,y)=03x+2y-y2=0…

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Q: Given the system of nonlinear DEs a' = -2x – 3y + xe" and y'= 3x - y +2- 2e": (a) Linearise the…

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A: Consider the provided question.

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Q: 2. Consider the nonlinear system of differential equations dx = r*y – xy dt dy = y – e" dt (a)…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

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A: Critical points

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A: Solving

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A: Hey, since there are multiple subparts posted, we will answer the first question. If you want any…

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A: dx/dt=x-2y dy/dt=4x-x3 Jacobian matrix A= 1-24-3x^20 Now at critical point (0,0) A = 1-240

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.