9. Let f(t) denote the number (in thousands) of fish in a lake after t years, and suppose that f(t) satisfies the differential equation: y' = 0.1y(5 – y) with the slope field shown below: y (in thousands) 5. 4. 3 6 (a) Determine what happens to an initial population of 6,500 fish. Does it increase or decrease? (b) Determine the numbers in the fish population that they will stay constant over time. (c) If the initial population is 1,000 fish, find the approximate of time when the lake has 4,000 fish in population.

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Q: 4. Eliminate the arbitrary constant 'a' in the differential equation: y – 2ay' + x2 = a? %3D

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A: The exponential growth model is given by: y=y(0)ekt,k>0

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A: Explanation  we have given the voltage change E across the heart satisfies the linear differential…

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A: In the question it is asked to calculate rate of change of weight for the bird with age.

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A: Partial differentiation is needed to be done after identifying M and N

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Q: 4 (a) Identify the homogeneity of the following second order differential equation and state the…

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Q: A ball at 1200 K is allowed to cool down in air at an ambient temperature of 300 K. Assuming heat is…

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A: Please see below pictures for detailed solution.

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Q: 22/ for the differential equation ģ =X+y if ylo)=1 s ind y (ood) by Using Euller modibied method…

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A: Given that, y' = 2y - x dy/dx = 2y - x At the point (1, 2) we get: dy/dx = 2(2) - 1 dy/dx = 4 - 1…

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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.