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: 3. Consider the second order differential equation _dx +7. + 6x = 0. dt2 dt (a) Convert the equation…

A: Given is the second order homogeneous second order differential equation: x''+7x'+6x=0 let us first…

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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Q: Form the partial differential equation by eliminating the arbitary from z=xy+f(x2+y2)

A: Form the partial differential equation by eliminating the arbitary from z=xy+f(x2+y2)

Q: Solve the system d = dt with a1 (0) = 1 and æ2(0) = -1. %3D

A: The given system of differential equation: x1'x2'=   0-1-1   0 x1x2+t0  ;        x1(0)x2(0)=1-1

Q: dt = 8x - x² Identify the equilibrium points Determine if the equilibrium points are stable or…

A: Since you have posted a question with multiple sub parts, we will solve the first four sub parts for…

Q: (du/dt)^3 – (du/dt)^2 – 2u = 0

A: Given: (du/dt)^3 – (du/dt)^2 – 2u = 0 Find : solve the differential equation

Q: For each equation draw a phase line (label the axis) labeling all critical points and their…

A: (a) Given the DE dydt=-y3+3y2-2y.

Q: Does the formula ду Ət əx ду 4x² represent an ordinary differential equation or a partial…

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Q: nsider the differential equation z' = (e" – 1)(x - 3)(5- a) • a) Find the equilibrium points. b)…

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Q: There are two types of differential equations - partial and ordinary, do you think what is the…

A: The main difference between an ordinary differential equation and a partial differential equation…

Q: Describe Differential Equation to Matrix Equation.

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Q: Find the most general real-valued solution to the linear system of differential equations [1 -2] a.…

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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.

Q: dx/dt=x(x2-4) Construct a phase-diagram of the nonlinear autonomous equation Ï. Determine the…

A: Image is attached with detailed solution.

Q: 2) The rate of increase in a bank account is 4% of the amount in the account; the initial deposit is…

A: a) The initial amount in the bank account is P=$1000. The rate of increment of the amount is…

Q: Find the linearly independent solution of the equation y"+xy'+y=0 around the point x=1.

A: We will find out the required solution.

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

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Q: y" + 4y' + 3y = x² Convert the equation into a first-order linear differential equation system with…

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Q: Find the general solution: y'- y |arctg2=1.

A: Hello, thanks for your question but according to our policy I am doing the very first question.…

Q: plot a phase diagram of the following system x'=2y y'=-x-y

A: We have to plot a phase diagram of the given system  x'=2yy'=-x-y

Q: 3 dw + xy + w = k dx2 2 +s + 2st = 0 dx (尚) ds dt dt y" – 5x(y')2 = e* + 1

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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: L" + 2x" – x' – 2x = et Write the equation as a 1st order linear differential equation system and…

A: Given equation is  x'''+2x''-x'-2x=e3t                                                (i) Let…

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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