Find the critical points of the system dx 14x – 2x2 – xy, dt dy 16у — 2у? — ху. dt

Q: Solve the following system dx -4x + 2y dt dy = -x - y dt

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Q: show that the given system is almost linear near the origin and discuss the type and stability of…

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…

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: dx 2. 2x + 2y dt dy = x + 3y dt

A: Since all the questions are different. So as per our guidelines, we are supposed to solve only first…

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 system below for x(t) and y(t).  2dx/dt +dy/dt − x − y = 1dx/dt +dy/dt + 2x − y = t

A: Consider the given system of equation.

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: Find the equation of the family of orthogonal trajectories of the system of parabolas y? = 2x + C. y…

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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: Consider the linear system: dx/dt = 2x + 6y dx/dt = 2x − 2y (a) Determine the type of the…

A: The equations are: dxdt=2x+6y anddydt=2x-2y The two equations can be represented by the matrix as…

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

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Q: Q5) Solve the system dx +y = et dt dy dt

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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/dt= -9x+4y dy/dt= -5/2x+2y (x(t), y(t))=?

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Q: solve the following system of equations: x'=dx/dt=7y+7e4t y'=dy/dt=5y-3e-5t x(0)=2 and y(0)=3

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Q: Obtain the genral solution. (D³ +5D²+7D+3)y=0 y=eX(C₁-C₂x) + С3e-³x + С₂e-³x Oy=eX(C₁+C₂x)…

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Q: Consider the following system. dx = -9x + 4y dt dy dt -5x + 2y 2

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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: 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…

Q: Use the method of undetermined coefficients to solve the given nonhomogeneous system. X(t) || dx dt…

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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)) =

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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: 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: 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: 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

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: Find the general solution of the given system. dx = 6x + y dt dy dt -2x + 4y (x(e), y(E))

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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: 3. Find the general solution of the system: dx = r+ y dx dy — 2л — у dt

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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: da dt = x – y dy = x + 2y dt

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Q: Determine the nature and stability of the equilibrium points of the system dx = x = y + x², dt dy…

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Q: Solve the system of equations below dx = 5x – 3y dt dy 11x – 9y dt %3D

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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: dx dt dy dt = 1 6 (x−1)(5−x− 6y x ) = y 20(1− y x−1) Find the nullclines  of the system

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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: Find the general solution of the given system. dx 2x + Зy dt dy = 6x + 5y dt 60°F Sunny e here to…

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Q: Q1] Solve this system of simultaneous diffe dx dt +7x + 2 equations. dy + 8y dt = 2et dy 7x+x+8+2y =…

A: Sol

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: (Find the general solution of the system 4 -2 x(t) + 1 dx(t) dt

A: The given system is: x'=4-211x+t1x'=Ax+g(t)

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: Use variation of parameters to solve the given nonhomogeneous system. dx = 2x - y dt dy 3x – 2y + 7t…

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Q: ()- Write the given linear system in matrix form. Assume X = dx 3 -2х + Зу + е' sin(2t) dt -t dy =…

A: The matrix form of given system is given as follows :

Q: 21/ solve one of the following Linear system: dx 1. - y = t? dt 2+ 4x = 1 dt

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