Consider an autonomous differential equation dy (y² – 9)(y +5) da Sketch the direction field of this equation. Find the equilibrium solutions and phase portrait of this equation. For every equilibrium decide if it is stable, unstable, or semi-stable. Sketch typical solution curves for this equation.

Q: dP/dt= 2P(1−P/25) (a) Draw a one dimensional phase portrait of the autonomous differential equation.…

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Q: dr + t 4tx 0 dt dt3

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Q: dy - 2y + 6 Find the solution of the differential equation. - dx 2.x + y + 2 ||

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Q: Find a differential equation whose general solution is y = c₁e²t + C₂e-2.

A: Note: Your general solution should be: .The differential equation for this general solution needs to…

Q: Solve the given differential equation by undetermined coefficients. begin mathsize 16px style y…

A: The solution is shown below-

Q: Q2: Find the fixed points and their stability for the following differential equation, and analyse…

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Q: (2xy + x)dy – [x² + y² + y + 1]dx = 0 When:x = 1; y = 0

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Q: A differential equation, a point, and a slope are given in photo. Sketch two approximate solutions,…

A: Given differential equation is dydx=24-x2 Point :- 2, π Slope Field:-

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Q: Find the differential equation associated to the equation: y = Ce" +C,e" - 5xe 1. 2. y = Cx'e +C,xe.

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Q: Consider the partial differential equation u; + uux = 8 + Uxx. Determine the order of this equation;…

A: The differential equation is given as ut+uux=8+uxx

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A: The objective of this question is to convert a second-order non-homogeneous differential equation…

Q: Instruction: Sketch the solution curve passing through each points. You can use computer software to…

A: We can solve as follows

Q: dy = -y + 2 with the initial value y(0) = -2 dx

A: Explanation of the answer is as follows

Q: 4. (2x – 5y + 1) dx – (5y – 2y) dy = 0

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Q: Find the general solution and sketch the phase portrait of z = ( 1 1 Z 4 -2

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Q: Find the solution of the dy Qoec() +y d'ifferential equation.

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Q: 5. A differential equation is if it can be written in the form f(y)d(y) = g(x)d(x)-

A: A differential equation is ORDINARY if it can be  Written in the form f(y)dy = g(x) dx .

Q: dy ycosy dt ||

A: Firstly we draw the graph then draw a phase line.

Q: solve the equation using differential equation linear in x and y: (2x-3y-5)dx + (3x-y-2)dy = 0;…

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Q: Solve the following linear system and sketch its phase portrait * = [¹ =1] x.

A: Here for a given homogeneous matrix linear system we have to solve it and then sketch the phase…

Q: -dx + 1 - x²y? dy. 1– a²y? dx = constant. help (formulas)

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Q: da dt dy 1 Int x + dt

A: Given Differential Equations are                                                         dxdt=y,…

Q: d the critical points and phase portrait of the given autonomous first-order differential equation.…

A: 25. Given the differential equation is                                          dydx=y2(4-y2).

Q: Determine the type of Differential Equation, then find the solution for it.

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Q: Consider the nonhomogeneous differential equa 1 "(x) + y(x) = e '+ sin a

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Q: y = x y' + (y')³

A: The given equation is first order non linear ordinary differential equation. Also it is clairaut's…

Q: Solve the following first order linear differential :equation 3Y + 3y – (7x + 1) = 0, y(0) = 2 |

A: the given differentital equation is the first order linear differential equation which is…