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

Q: الإنجليزية Q3: It is required to find the general solution of the following system dx =y+z dt (1) dy…

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A: dxdt=3x+2y-y2=f(x,y)dydt=-2x-2y+xy=g(x,y)Now, put f(x,y)=0 and g(x,y)=03x+2y-y2=0…

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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: 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: Solve the given initial value problem. dx dt 7x+y; x(0) = 3 dy dt = - 6x +2y; y(0) = 0 The solution…

A: To solve the given initial value problem.dxdt=7x+y;  x0=3dydt=-6x+2y;  y0=0

Q: The Volterra- Lotka system for two competitive species is  dx/dt = x(-Ax -By +C) dy/dt=y(-Dx-Ey+F)…

A: Given- The Volterra- Lotka system for two competitive species is  dxdt = x-Ax - By + Cdydt = y-Dx -…

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

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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: For the system below dt = x + 2y = -2x + y (a) Find the general solution; (b) Sketch (by hand) the…

A: The vector equation is x'y'=12-21xy Obtain the eigenvalues: A-λI=1-λ2-21-λ=1-λ2+4λ1, 2=1±2i The…

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

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Q: 4. od to solve the given system dy (a) dt d* – 2x - - y = 6et, 2 - 3x + - 3y = 6e"; %3D dt dt x(0) =…

A: Given :-  Use the Laplace Transform dxdt -2x - dydt -y =6e3t2dxdt -3x + dydt -3y =6e3t

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

A: Given system is dxdt+dydt=2x+2y+1           (1)dxdt+2dydt=y+3                    (2) let the…

Q: Use variation of parameters to solve the given nonhomogeneous system. dx 2х - у %3D dt dy 3x 2y + 8t…

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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: Solve the non homogeneous system of simultaneous diferential equation dx/dt+2dy/dt-3x+4y=e^2t…

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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: b) Solve the following initial value problem, where all constants are strictly positive. d²x dx dx…

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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: Find the complete solution using classical method to the system (D2 +6 D+ 25) y(t) = (D+ 3) x(t) for…

A: The system is D2+6D+25yt=D+3xt Initial condition is, y0+=0dydt0+=2Input xt=utTo find the complete…

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Q: Consider the system dx х — ху — 2? dt dy xy – 2y dt where a and y denote the sizes of two…

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Q: Find the general solution of the given system. dx = 3x+4y dt dy = 8x+7y dt (x(t), y(t)) =

A:

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: 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: 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: For the system below, find the particular solution with initial condition (x(0), y(0)) = (4,7). dx…

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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: Use the method of undetermined coefficients to solve the given nonhomogeneous system dx = 5x + 9y +…

A: Given system of differential equation is dxdt=5x+9y+7dydt=−x+11y+21 Write the given system of…

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

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Q: Solve the given initial value problem. dx/dt = 7x+y; x(0)=1  dy/dt=-6x+2y; y(0)=0 The solution is…

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Q: Consider the system: dx/dt=4x(1-2x)-xy dy/dt=2y-4xy (a) Are these species predator-prey or…

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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: 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: For the system below a. Find the equilibrium points. b. For the equilibrium point (1,1) solve the…

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Q: Consider the system dx dy 1+3y, dt -1– 5x? dt a) Find all the critical points (equilibrium…

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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 dt  =  7x + 5y   dy dt  =  −2x + 9y

A: The given differential equation can be written as: dxdt=7x+5y⇒D−7x−5y=0​…

Q: Use variation of parameters to solve the given nonhomogeneous system. dx 2х - У dt %3D dy Зх — 2у +…

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

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Q: Use the method of undetermined coefficients to solve the given nonhomogeneous system. dx 2x + Зу - 8…

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Q: For the following system: dx dt dy = x – x* dt (a) Find equilibrium point(s) of the system.

A: (a)  We have given system of differential equations       dxdt=-y4       dydt=x-x3to find…

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

A: Given

Q: Consider the system dx х — ху — х? %3D dt dy xy – 2y dt where x and y denote the sizes of two…

A: Hey, since there are multiple subparts posted, we will answer the first question. If you want any…

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