dy, = y2 dt 9 Consider the linear system dy2 -Yı dt Find the solution of this system which satisfies the conditions y, (0) = 0, y, (0) = 1 Find the solution of this system which satisfies the conditions y, (0) = -1, y,(0) = 0 Show that the two different solutions found in a),b) both represent the same path.

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A: Given: Let consider the given system of equations is  dxdt=x1-x5-ydydt=y1-y6-x Introduction:…

Q: /5 -4 0) X' 1 0 2 2 5 ||

A: First find the Eigen value of the matrix:

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A: Given functions are f(x,y) = xy + x2 - y3 - 1g(x,y) = x + 2y - xy2 - 2

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A: Newton's method is an iterative method for solving a system of nonlinear equations. The idea is to…

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A:

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A: 2.(B)The given non-linear system is .Find the all equillibrium solution as follows.Put  as…

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A: We can solve this using given information Given information x1=3x2

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Q: Determine if the nontsivial Soluton ystem has a X,-3>c + 7)C3=O -2x,+ Xz -4x3=0 923=0 Xi + 2x2 +

A: To determine if the system has a non trivial solution.

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A: y=x+4 Graph

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A: Use substitution method to solve for x,y,z

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A: Given: The given second order differential equation is y'' + 5 y' - 6 y = 0

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A:

Q: Consider the nonlinear system equations X = x2-e-1, X2 = sin(x,-x2) -x,' +ux,, %3D y = x1 + X2. If u…

A: We will linearize the system by calculating its Jacobian matrix at the given state values.

Q: 7- What can we say about the linear system: x + 2y – 3z = 1 2.x + 5y – 8z = 4 3x + 8y – 13z = 7 The…

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Q: Q3) An electrical netuark can be modelled using a system of first order linear differenhial equation…

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Q: *, = ax, - Bx,X2 iz = -yx2 + 8x,x2 A) Linearize the prey-predator system above about x = B) Decide…

A: For the solution follow the next steps.

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A: By using row transformation, we check the behaviour of linear system.

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A:

Q: *, = ax, - Bx,X2 i2 = -yx2 + 8x1x2 A) Linearize the prey-predator system above about x = B) Decide…

A: For the solution of this problem follow the next steps.

Q: U₁ + Ux+Vx = 0, v₁ + UxVx = 0, u(x, 0) = u(x), v(x,0) = vo(x).

A: Given clear explanation below.

Q: Convert the following linear equation into a system of first order equation of the form y' = P(t)y +…

A: