The differential equation dx/dt = 100x(x- 5)+ s models a population with stocking at rate s. Determine the depen- dence of the number of critical points c on the parameter s, and then construct the corresponding bifurcation diagram in the sc-plane.

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A: hintddxtan-1x=11+x2 or,∫11+x2dx=tan-1x

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A: We can apply fundamental theorem of calculus here.  The second fundamental theorem of calculus…

Q: is poured into the tank a te of 2 liters/min. Let y(t ial model for (t) and gol

A: The figure as,

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A: Given: y=e14xy=1

Q: 1 dt. 1+ vt Let G(x) Find G'(9).

A: Given that: G(x) = ∫2x211+tdt

Q: 3. Given the following graph and A(x)= [f(t) dt, find: A(4)= 4 y=f(t) 3 A(6) = 1- A(10)= A'(x)= -2

A:

Q: Calculate the increment and differential of the function y=x+2/x+1 at the point x=0 when Δx=0,1.

A: The increment of the function: y=f(x) is calculated using the formula: ∆y=fx+∆x-f(x). The…

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A: We have been given a linear differential equation dydt=t−y ______(i) (As y′=dydt)We have to find the…

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A:

Q: Consider a pond that initially contains 10 million gal of fresh water. Water containing an…

A:

Q: a) How is ds/dt related to dx/dt if y is constant? ds/dt=___(dx/dt)

A: Consider a function S with variable x and y as constant. S=fx+ywhere, fx=function with x as…

Q: Find the differential dy. (a) y = xv8- x %3D dy %3D (b) y = (1+ x)7 dy

A:

Q: Find the second differential of the function y=x2cos2x.

A:

Q: Find the differential dy of the function y = 4x²-x+ 3 Select one: O a. (8x-1)dx O b. (x²-x² + 3x) dx…

A: Solve for the differentiation

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A:

Q: Consider the first order linear equation И u' (t) = 3 - 7/2/₁ t2 Find an integrating factor u(t) for…

A: