Recall that cos(x) = cos(x-л) and consider the differential equation on the domain x Є [0,л], у Є [0,π]. d x(t) = = sin(x) (cos(x)+cos(y)) Then, d dt (t) = sin(y) (cos(x) — cos(y)) • sketch the 6 nullclines of the differential equation in this region, • determine any equilibria, ⚫ determine the linear stability of equilibria points using the Jacobian matrix.

Q: Find y' if y= cos (X-1) X-1

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Q: 5 Find y' if cos (Xty) =

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Q: JO (5) Find the derivatives (a) d # t ( * cos(2³) dz + 35e) 4

A: Since you have posted multiple questions i can do first question as per our company guidelines.…

Q: Solve the IVP y"(1) +y'(t)- 2y(1)= 2e' sin(t), y(0) = 1, y'(0) = 1. %3D

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Q: e" sin°(2x) (d) y = In 2x2 + 1

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Q: Compute the following derivatives. Show all your work and indicate which differentiation rule(s) you…

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Q: 3y' –4x²y+ xy = -5 %3D

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: -1 Find the derivative of the function: y=6 sin ¹¹ (x²). y'= y'= O y'= 12x y'= -X 2x 2 + X 12x 4 4 X…

A: Given y =6 sin-1 (x2 )

Q: y" – y' – 2y = sin 3t y(0) = 1 and y'(0) = -1

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Q: If f(x) = x^2 sin(3x), find the differential dy

A: Consider the given: fx=x2sin3xy=x2sin3x Differentiate w.r.t. "x", dydx=ddxx2sin3xApply the Product…

Q: (1+x)y' + y = cosx; y(0) = 1

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Q: If y(t) is the general solution for the equation: y' + y = sin(t), y(pi/2) = 0 Then, y(0) = ? a)…

A: Consider the differential equation  y'+y=sint,           yπ2 = 0

Q: If f(x) 3 sin '(2), then f'(x)-

A: Given that: f(x)=3sin-1(x5)

Q: (7) Suppose x4 + yª = 5 (a) Use implicit differentiation to find y' = . Simplify your answer. dy (b)…

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