Construct an autonomous first-order differential equation dy/dx = f(y) whose phase portrait is consistent with the given figure. | (y- 1) (y– 3) (y– 5) dy y 5r 3

Q: Draw a phase line for the equation y' = y³ (y – 5). If y(0) = 2, what is the lim y(x)?

A: The phase line for the differential equation is shown in the figure. There are two points where the…

Q: a) Solve differential equation dx (y² – 4)(x – 1) = (x + 1): dy

A: Solution of the problem is given in the next step.

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Q: x' = Ax A = 1 -1 13

A: , where .We have to solve the following system and draw the phase portrait

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Q: 8. Determine the stability of i = 1 01 x and sketch its phase portrait. 2

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: 2 - -1 -

A: We have to find an autonomous first order differential equation dydx=fy whose portrait is consistent…

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Q: x=5cos(t) y=8sen(t) is a parametric solution of the following ordinary differential equation?

A: Here dy/dt=8cos(t)  And dx/dt=-5 sin(t) Divide both and we get  dy/dx= (-8/5) cot(t) and from given…

Q: 3. Show that the equation (6ry – y*)dx + (4y + 3x² – 3xy²)dy = 0 is exact. Hence solve the equation…

A: Solution:

Q: Construct an autonomous first-order differential equation dy/dx = f(y) whose phase portrait is…

A: Consider the given figure. From the figure, it can be noted that the critical points are 0 and 2.…

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A: Consider the autonomous differential equation: dydt=g(y) If for the equilibrium point y=a 1) If…

Q: Solve using the non-exact linear differential equation  [ytan(x)(cos(2x))-1]dx+csc(2x)dy=0 when…

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Q: + √" y(7) cos(t — 7)dr, y(0) = 1. 2. Solve y' (t) = cos(t) +

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Q: (5) Solve the IVP:dy - y = e* cos(2x), y(0) = 2 dx

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Q: Determine the direction and magnitude of the phase shift in f(x) = 3sin(x + n/6) - 2 O n/6 O None of…

A: We have to find out

Q: 3. dy/dx y²– 2y (a) Identify the equilibrium values. Which are stable and which are unstable?

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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: Solve  y′ + 2y cos(2t) = 2 cos(2t), y(π/2 ) = 0

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Q: Please solve the following differential equation: dy (e2x + 4) – y dx (х — у) (4х + у)dx — x(у —…

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Q: Consider the differential equation y' = 1 - y. (a) Find equations for the isoclines corresponding to…

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Q: Solve the initial value problem for initial values 2 0 y' = ( 1₂9₁ ) y, у, 1 1 a) y(0) = ( −¹₁),…

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Q: Find the conic equation which satisfies the separable differential equation dydx=−18x/y dy/dx with…

A: The given differential equation is dydx=-18xy with initial condition y1=5. To find the conic…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.