7. Sketch a phase portrait for the system x₁ = 4x₁ + 10x2, x2 = x1 - 5x2. You should sketch several typical solution curves in the ₁2-plane.

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

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Q: phase plane of the system

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Q: > < | 1. ä ' = [ 11 -10 10 -1 | 2. z' = [ {} 5 4. a' -2 | 3. z' = [ 2 -1 [ 8] 3 189 TEB 18 -13 107…

A: Four systems of differential equations along with their phase planes are given.

Q: Solve the system Ÿ' = AŸ + Ġ for A

A: a0 A = 7-143 , B = 5505 , P = 122-1Then p-1 = 1-1 -4 -1-2-21               = 1-5 -1-2-21…

Q: 2. Find the general solutions of the system 13 2=(² -2 Sketch its phase portrait and identify the…

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Q: x' Construct the phase plane for the points (2,2), (2,0), (2,-2), (0,2), (0,-2), (-2,2), (-2,0) and…

A: According to questionWe have to draw the phase plane for the given points.

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

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Q: 2) Consider the predator-prey model 2 x'= ax -x²-bxy 2 y'=cy - cy² + xy where all the parameters are…

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Q: х2у" + x(x-1)у' + (1-x)у %3D 0

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Q: Use the variation of parameters formulas to find a general solution of the system -3 2 et y' 2 -3 2…

A: The method of solving a nonhomogeneous linear system of differential equations is the following.

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Q: Solve the system using the elimination method 5x'+y" -y + =t x" - 4x - 2y' = -2...

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

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Q: Consider the system x' = Ax + g(t), where -3 A = and g(t) %3D (a) Find the general solution.

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Q: Solve the system -6 -2 =B]. dx 20 6 dt 2 -[:] -2 with x (0) = x2= 8 Give your solution in real form.…

A: The given system is   with initial condition               Let  The characteristic equation…