[14] For each of the following equations, find all equilibria; • find general solutions; solve the initial value problem with initial condition ₁ (0) = 2, x₂(0) = 1; sketch the phase portrait, identify the type of each equilibrium, and determine the stability of each equilibrium. 10 () [2] - [39] [21] = •4-140+3 (b) = -5 -7 + X2 3

Q: FIND THE GENERAL EQUATION OF THE FOLLOWING SOLUTION: y" = 12 %3D A.

A: A) The differential equation is given as y''' = 12 On integrating both sides , we get ∫y''' = ∫12y''…

Q: Determine which one of the following equations are lin identify the nonlinear terms. 2Vã – yxi+ zxi…

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Q: Solve X x (t) = y(t) = - 17 ²7] [7] (0) - x (0) = 4, y(0) = 19

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Q: Suppose the following equations describe the relationship between the long-run shares of spending in…

A: R = 0.05 We have to find the intrest range and long run shares of spending in gdp C/Y  = 0.7 - 0.2(…

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Q: Please answer all and graph

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Q: dy Solve the initial-value problem for y as a function of x. (16-2²) d = 1, y(0) = 9 y +9 X

A: The given initial value problem is:

Q: (c) Solve the following IVP by separating variable. 2(y - a)da + (3a + 4r + b)dy = 0 Using initial…

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Q: If pressure is maintained such that x = 0.042 and given that -0.6 <w< 0, find w using i. the…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 2. Find the solution y = f(x) to the equation x² + y²-2³=0 near each of the following points: (a)…

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Q: Find the general solution to the equation y4) – 6y" + 9y" = 0. NOTE: Use c1, c2, C3, and c, as…

A: We can rewrite the given equation as y''(y''-6y'+9y)=0 Put y = erx then y' = rerx and y'' = r2erx

Q: dy 3. Plot the slope field for the differential equation dx = y2 – x and sketch the solution for the…

A: Introduction: Slope fields (also known as direction fields) are a graphical representation of the…

Q: (a) Find the general solution of the following equation: y(3) + 5y" + 3y' – 9y = -27x +9+32e". %3D

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Q: (D3 - 3D - 2)y =0; when x =0, y=0, y' = 9, y" = 0. 2x y = (-2 + 3r)e¯*+2e² B В y = (-1+ 2x)e2* + 2e…

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Q: For butter pecan ice cream, the supply function is given byp = S(q) = 0.4q and the demand function…

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Q: Solve the DE. (x³ + xy²-y)dx + (y³ + x²y + x) dy = 0 O arctan(‡)=C − x y O arctan (=) = C - x² - y²…

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Q: Find the solution. (D3 - 3D - 2)y =0; when x =0, y=0, y' = 9, y" = 0. A y = (-1+ 2x)e-2*+ e 2x B y =…

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Q: For the system, 6 -1 Y' = Y 5 4 Write the natural period of the oscillations, round the answer to…

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