H2. Classify the critical point and sketch the phase portrait of the following systems of first order equations dx = x+3y, dt dx — 5х — у, { { (i) (ii) dy = 3x+y; dt dy 3x+y. dt

Q: 3. For the competing species population model dx —D х(-х — Зу + 150) dt dy %3D У(-2х — у + 100) dt…

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Q: Solve the system -1 dx dt with x (0) 2 x2 = -1 1 2 [:] 1 x Give your solution in real form. x1 = An…

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Q: The values of C, and C₂ so that y(x) = C₁x + C₂ (-) satisfies the two conditions y(1) = 1 and y'(1)…

A: Given: yx=C1x+C2-13x2 To find the values of C1 and C2 such that y1=1 and y'1=-1.

Q: Obtain the general solution of the following equations: 1. Dx + (D-1)y=5 2(D+1)x+ (D+1)y=0

A: Note: As you uploaded multiple questions, but according to Bartleby guidelines I will answer only…

Q: Consider an autonomous differential equation -f(y) for which the graph of f(y) vs y is shown below.…

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Q: Problem III: x'y+ yz + xz' =9; P= (1, 4, 1) Find the following partial derivatives at the point P:…

A: To find the following partial derivatives .

Q: t°yı + 2y2 + sec(t), sin(t)y1 + ty2 – 4. This system of linear differential equations can be put in…

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Q: dx dt Y 2x. dy dt X y. (a) Find x nullclines, y nullclines and all equilibrium points. (b) Construct…

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Q: Consider the nonhomogeneous linear equation y" +9y' g(t) with the complementary solution y,= c1y1(t)…

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Q: Using the given substitutions, find the solutions of the following equations. dy x+y dx 1-х-у (а) z…

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Q: If y, and y₂ are linearly independent solutions of t^2y" + 5y' +(2+t)y = 0 and if W(y₁, y₂)(1) = 3,…

A: Given differential equation is t2y''+5y'+(t+2)y=0   Also, given y1, y2 are Linearly Independent…

Q: Determine all equilibrium solutions and classify as stable, semi-stable, or unstable. dx =(x²-4)² dt…

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Q: For the phase portrait shown below 1 -1 -2 -3 -4 -5 Classify the equilibrium point (0,0). Give type,…

A: All the trajectories are attracted towards the equilibrium point (0,0)

Q: Find all the first order partial derivatives for the following function. f(x, y) = 9x - 5y2 - 3 . -…

A: The function is given by fx, y = 9x-5y2-3 To determine: The expression of ∂f∂x and ∂f∂y

Q: x = 2x y = x + y

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Q: (2х — 1) dx + (5у + 9)dy 3D 0

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Q: A. First-order homogeneous equation: (xe + y) dx- xdy 0 B. First-order linear equation: x cos x 2y…

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Q: If y = 2² is one solution of x²y" + 2xy' − 6y = 0, find the other linearly independent solution.

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Q: Classify the equilibrium points and sketch the phase line: dx = x* + x³ – 6x² dt

A: Autonomous Differential Equation: A differential equation of the form,…

Q: Consider the system dx/dt = x(2-x-y) dy/dt = y(y-x2) a. Determine and sketch the…

A: Given: dxdt = x(2-x-y) dydt = y(y-x2) for the nullclines. dxdt = x(2-x-y)=0 x=0 (or) y=2-x------(1)…

Q: dx dy 1. " + y = x , dt = 3y dt |

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Q: Find all the first and second order partial derivatives of f(x, y) = −2 sin(2x + y) + 8 cos(x − y).…

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Q: (x=-5x+2y j y = x-6y

A: We have given system of DE'sIt can be written asLet,  called as coefficients matrix.