Can you calculate X(t) = exp(At) and show the matrix satisfies the differential equations. And please answer the final part - characterise the trivial equilibrium and sketch the phase portrait in the new coordinates.

Q: What is an autonomous differential equation? What are its equilibrium values? How do they differ…

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Q: there a way to check if the equation you find after applying the initial condition is correct?

A: Let  Given that dy/dx = 2x (y − 1),.      y(0) = y0. And from solved answer The general solution is…

Q: equilibrium

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A: (a) Given the DE dydt=-y3+3y2-2y.

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Q: Describe Differential Equation to Matrix Equation.

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Q: Draw the phase line to the differential equation: dy/dt = -2(y-4) * y^(4) * (y+1) = f(y).

A: Given: dydt=-2(y-4)y4(y-1) To draw: phase line.

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A: Image is attached with detailed solution.

Q: Transform the given differential equation into an ferential equations. equivalent system of…

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Q: True or False The system dx/dt = 2y dy/dt = sin(xy) has only one equilibrium point.

A: We need to equate both the derivative to 0, to calculate the equilibrium points.

Q: Consider the DE dy/dt = y^(3)*(y −1)2(y + 2). Draw the phase line and a graph showing the long-term…

A: This is a problem of the autonomous differential equations.

Q: Solve the system [: 16 -36 dx dt 6. -14 with the initial value 13 x(0) 5 -5e^(4t)+13e^(-3t) x(t) =…

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Q: Consider the non-linear differential equation * =- x+ y – 1 ў 3 2х + х3. Draw the nullclines and a…

A: Regression Analysis:              Regression analysis helps to estimate the changes when…

Q: his is a practice question from my Differential Equations course: Show directly that the given…

A: Given functionA set of functions are linearly independent if Wronskian is non zero.and dependent if…

Q: x' = Ax where A = 3 2 -2

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