Find all limit cycles of system x₁ =−x₂ + x₁(1-x² - x²) (2 - x² - x²), x₂ = X₁ + X₂(1 − x² − x²)(2 − x² − x²), - determine their stability, and then sketch the phase portrait of the system.

Q: - (4y" + fy) = -A with y(-1) = -2, y(-1) = 1, y"(-1) = 0 Use x1 = y, x2 = y', and x3 = y". x + with…

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Q: 4. A = [ 5 7 5 ²]. b = = ['₁ 5 12 17

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Q: x' = Solve y"-5y'+6y=0 by writing it as a system Ax and solving that system.

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Q: Please answer all and graph

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Q: Find the general solution of the given system of equations. Solve using similarit transforms. x' =…

A: Given,           x'=2-13-2x+1-1et

Q: Express the system of differential equations in matrix notation. x' = (e ¹)x+ (at + bt³)y y' = (tan…

A: The given system of equations is ,           x' = (et)x + (at+bt3)y             y' = (tan t)x + (…

Q: y=1-x^2 y=x^2-1 Find the two solutions of the system when x0

A: Given: y=1-x2 and y=x2-1 To find the solution of the given system we have to equate both the…

Q: 3. Write the given system of differential equations in the matrix form and find exponential…

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Q: Find the number of equilibrium solutions of the r x' = x(y-2) โม่ = x − y

A: x'=x(y-2)y'=(x-y) Equilibrium solution of a system of differential equation X'=AX are those solution…

Q: Take the system Find a particular solution of the form *₁(t) = x₂ (t) = help (formulas) = v cos(4t)…

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Q: 6. A = 4 7 3 6 b = 10 5

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Q: Solve the system of linear equations with the given initial conditions. x' (t) = [1 2] x |x(t) with…

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Q: 3 ve the nonhomogeneous system tY' = (²2 =²) x + (-²₁) -21). Y (2-2)

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Q: x' = 4x + y + 2t, y' = −2x + y

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

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Q: 3. Solve the system by using the matrix exponential -2 3 x' = [ X 5 -1 2 x (2) = (2] 4

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