Determine whether the below systems are linear or non-linear. a. dy/dt + 2y(t) = P(t) b. dy/dt + 3ty(t) = t?f(t)

Q: please use laplace transform for the below linear system to solve system of equation. x(t)+6y'(t)=1…

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Q: Determine the nature and stability of the equilibrium points of the system dr = x=y+z², dt dy 12r -…

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Q: Find the general solution of the given system. dx 8x + 13y dt dy = -2x + 10y dt (x(t), y(t)) = |

A: We first write the given system in the form        X'=AX Then we find eigen values and eigen vectors…

Q: i(t) = y – x³ ý(t) = -x³ – y3 a) Is the origin stable or asymptotically stable for the linearized…

A: (a) Given equations are, To find the stability, And,

Q: If the input applied to a linear time invariant system is x(t) and its impulse response is h(t),…

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Q: Solve the given linear system dx = x + 2y, dt dy 2*+y 1 dt II

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Q: Find the general solution of the given system. dx = 4x + 5y dt dy 10x + 9y dt (x(t), y(t)) =

A: X(t) = C1e14t +C2e-t  Y(t)= 2C1e14t - C2e-t

Q: Find the general solution of the given system. dx 4х — у dt dy = 16x – 4y dt (x(t), y(t) :

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Q: An LTI system has impulse response h(t) = (1/t“) u(t – 1). Show that the system is BIB0 stable if a…

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Q: True or False The following system dx/dt = − cos x sin y dy/dt = 2x^2 + sin x cos y is a…

A: Hamiltonian system condition  ∂f∂x = -∂g∂y

Q: dx 4x +2y+e* +2t dt 17. Write the system in matrix form: dy -x +3y-et dt 4 2) X + -1 3) 4 2) X+e +2t…

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Q: Determine all critical points of the system of equations dx = 2x + x? + y?, dt dy 2y – xy. dt %3D -

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Q: Consider the following system on (-1,∞0) × (–1, 0), 2y 2x 1+ Y 1+x 1. Find all the equilibrium…

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Q: Find the general solution of the given system. dx/dt=6x+y dy/dt=-2x+4y

A: The given system in matrix form

Q: Use the method of undetermined coefficients to solve the given nonhomogeneous system. dx/dt = 2x +…

A: The system of equation is given as dxdt = 2x+3y-8dydt = -x-2y+6 It can be rewritten as X' = 23-1-2X…

Q: Consider the linear system : dx 2x – 2y %3D dt dy - 2x + y with initial conditions x(0) = 0 and y(0)…

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Q: A dynamic system in continuous time is specified as in, dx(t) / dt =-2x(t) + 4 and dy(t) / dt =…

A: Given equations are dxtdy =-2x(t) + 4    ....* and dy(t)dt= 3x(t) - y(t)    ...** To find the value…

Q: transform the equation into a systems of first-order equation: 2y(4) - et y' + 2ty = cos(t) y(0) =…

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Q: Solve the system dx 4x %3D dt dy 3y + z dt dz -y + z dt

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Q: Find the general solution of the given system. dx =x +2y dt dy = 4x + 3y dt St -t+C2 2 a. e 1 b. St…

A: here we will find general solution of given system of equations,

Q: b) Solve the given system dx = x + 2y, dt dy 1 dt x+y 2

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Q: Consider the equilibrium O of the continuous-time system given by å = Ax,where A E R²×". Which of…

A: This is a problem of the Dynamical system, a system of the differential equations.

Q: the given system of differential equations to a first-order linear system. dx/dt  - ty  =  cost…

A: We have to change given system in first order system: Given system is:

Q: Find the general solution of the given system. dx -9x + 4y dt dy X+ 2y 2 dt (x(t), y(t) =

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Q: By using the Liapunov function V(x, y, z) = x² + y? + z?, show that the origin of the following…

A: To show that for the Lyapunov function the origin of the given system is asymptotically stable. If…

Q: Find the general solution of the given system. dx 4x + 5y dt dy = 10x+9y dt (x(t), y(t)) = =

A: The solution of system of differential equation is solved below

Q: Find the general solution of the given system. dx = 2x + 3y dt dy = 6x + 5y dt (x(t), y(t))

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Q: Find the general solution of the given system. dx 3D 3х — у — z dt dy - х + у — z dt dz = x - y + z…

A: Given that,

Q: Find the general solution of the given system   dx/dt = -4x +2y   dy/dt = -5/2x+2

A: Here we have to find the general solution of the given system,  dxdt=-4x+2y ......................…

Q: For the following system dx dy + dt = et dt -d²x dx dt2 + x + y = 0 dt

A: Given the system of differential equation is…

Q: Find the general solution of the given system. dx = 4x + y dt dy = -2x + 2y dt (x(t), y(t)) =

A: Given system of equation, dxdt=4x+ydydt=-2x+2y Write the differential equation in the matrix form…

Q: Consider the system: dx/dt = 2x + 2y dy/dt = x + 3y For the given function P(t) = (x(t), y(t)),…

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Q: Find the general solution of the given system. dx = 2x – 2y – 2z dt dy :-x + 2y dt dz -x + 2z dt

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Q: Find the general solution of the given system. dx Зх + 4y dt dy 8x + 7y dt (x(t), y(t)) =

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Q: Find the general solution of the given system. dx - = x + y - z dt dy Зу dt dz = y - z dt (x(t),…

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Q: Find the general solution of the given system. dx 4x + y dt dy = -2x + 2y dt 14t (x(t), y(t)) = |…

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Q: Find the general solution of the given system. dx = 4x + 5y dt dy = 10x + 9y dt

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Q: Let   dx/dt =   x2y3           dy/dt  = -x - y - (xy4)/2 be a dynamical system.   Is  L(x,y) =…

A: Given function is, dxdt=x2y3dydt=-x-y-xy42......(1) Lx,y=x22+x2y44.....(2) For the proper Lyapunov…

Q: 1. Use operator / elimination method to solve the given system dx dy + = 2x + 2y + 1 dt dt dx dy y +…

A: Since you posted multiple questions, we will solve first question for you.

Q: Find the general solution of the given system. dx = -9x + 4y dt dy x + 2y 2 dt (x(t), Y(t)) = %3D II

A: Introduction: The system of first order differential equation is generalized as dxdt=fx,ydydt=gx,y…

Q: Find the general solution of the given system. dx = 9x - y dt %3D dy = 5x + 5y dt (x(t), y(t))

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Q: Consider the non-linear system dy a² + xy – x, dt de yx – y² – y. dt How many equilibria does it…

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Q: For the following system of DE: dx dy et dt dt -d?x dx dt² + dt +x + y = 0 The solution function…

A: To Determine :-  The system of ordinary differential equations :- dxdt + dydt = et- d2xdt2 + dxdt +…

Q: Find the general solution of the given system. dx = X + y- z dt %3D dy бу dt dz = y - z dt

A: The solution is given as

Q: Write the given linear system in matrix form. Assume X = y dx -t — - 2х + Зу + e' sin(2t) dt dy -t =…

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Q: Find and classify the critical point of the linear system. dx/dt = -3x-y-19 dy/dt = 13x+y+69

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Q: (c) Identify the unit impulse response of an Linear Time Invariant Continuous system specified by…

A: Given: (D2+6D+9)y(t)=(2D2+9)x(t)

Q: dx/dt=x-2y dy/dt=4x-x3 Using the method of linearization, determine the nature and stability of…

A: dx/dt=x-2y dy/dt=4x-x3 Jacobian matrix A= 1-24-3x^20 Now at critical point (0,0) A = 1-240

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.