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Wolfram Mathematica coding

Help to write some Wolfram Mathematica for those statement:

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Suppose that demographic studies show that each year about 6% of a city's population moves to the suburbs (and 94% stays in the city), while 4% of the suburban population moves to the city (and 96% remains in the suburbs). In the year 2000, 59% of the population of the region lived in the city and 41% lived in the suburbs. Derive a function to give the population distribution for any year in the period 2000-2050. For simplicity, ignore other influences on the population such as births, deaths, and migration into and out of the city/suburban region. Use two methods: 1. Markov matrix multiplications 2. linear combination of eigenvectors For each method, construct a list of population distributions for the years 2000-2050. (Obviously, the two lists should contain identical values - but may be structurally different.) Plot the list. From the eigenvector approach, determine the stable population distribution (n->\[Infinity]).

2.

2.1 Compute the general solution to : dy/dx+(1/x)y=sin x

2.2 Solve the initial value problem: dy/dx+(1/x)y = sin(

Skills: Mathematics, Matlab and Mathematica

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